I have more to say about the possible changes to Kantian Philosophy and the addition or not of the question of discontinuity systematics in the monoisolatable object on the better understanding of Chemistry that Georgi Gladyshev presents when quoting the classics as in this most recent communication from him below but I will let him speak more for himself. I will indicate the modifications if any in answer to Tony on the "quantum discretum"(sp?) of Kant to be edited into an already existing post.
Here is another "large quote" that perhaps indicated where we had some issues on the chemistry of life?
[Quote]
The Second Law of Thermodynamics and Evolution
of Living Systems
Georgi P. Gladyshev
International Academy of Creative Endeavors, San Diego, USA
Corresponding address: N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, Kosygina 4, Moscow, 117977, Russia
Abstract: The classical formulations of the second law of thermodynamics are presented. Some mistakes in the understanding the physical meaning of this general law of nature are noted. It is asserted that many misunderstandings of the second law of thermodynamics are related to terminological confusion and the underestimation of the theory developed by J.W. Gibbs and other founders of "true thermodynamics," which is impossible to disprove. To a certain approximation, R. Clausius and J.W. Gibbs' thermodynamics is applied to describing the evolution of living systems. This is possible due to the law of temporal hierarchies and the premise that the functions of state of living systems have real physical meaning at practically all hierarchical levels and at every moment of time. Making no pretensions to perfection, the author offers some advice to researchers dealing with thermodynamics. The author believes that, when considering thermodynamic problems, "ambiguous" terms and definitions should be clarified preliminarily in order to preclude possible misunderstandings. It is also advisable to refer to the classical works (including textbooks and encyclopedias) that the authors of publications have used. This will allow the correctness of the results reported to be estimated at least preliminarily.
Keywords: Second law, thermodynamics, chemical thermodynamics, entropy, Gibbs function, Gibbs energy, full differential, law of temporal hierarchies, evolution, living systems, quasi-closed systems.
AMS Mathematical Subject Classification: 74A15, 80-06, 80A50
PACS: 05.70.-a, 64, 82.60.-s, 95.30.Tg
" the true and only goal of science is
to reveal unity rather than mechanisms"
Henri Poincar
Classics of science actually enunciated the second law of thermodynamics, one of general laws of nature, in the first half of the 19th century. Well-known formulations of this law are associated with the names of N.L.S. Carnot (1824), R. Clausius, (1850), and W. Thomson (Lord Kelvin) (1851). Although the formulations themselves are different, mainly because of the difference in phrasing, they may be considered equivalent. Many authors have attempted to change or improve the formulations as regards their physical meaning, yet none has succeeded. The meaning (essence) of these formulations has not been disproved to date [1—23]. However, new concepts have extended the possible applications of the second law of thermodynamics to different sciences, especially chemistry and, as it turned out later, biology. This became possible mainly due to J.W. Gibbs' works performed in 1873—1878. To a certain approximation, the methodology of Gibbs thermodynamics [2] has been extended to date to all hierarchies of natural systems, which are generally open ones [17]. The discovery of the law of temporal hierarchies, which may be considered a new general law of nature, has determined the extension of Gibbs's theory to living systems [17, 22—28]. This law [17] makes it possible to apply thermodynamics (more precisely, the hierarchic thermodynamics of quasi-closed systems), to all hierarchies of the real world, particularly, living objects and biological systems, to quite a good approximation. I believe that the discovery of this law confirms the universality of classical thermodynamic methods, and the name of Josiah Willard Gibbs even more vividly symbolizes the future of science that confirms the validity of general laws of nature as applied to the evolution of all material systems at all organizational levels of our world. Advances in classical thermodynamics (as well as approximate thermodynamics, i.e., the quasi-equilibrium thermodynamics of quasi-closed systems) are described in a number of textbooks and monographs. They are certainly numerous; I would especially recommend the works [1—17], which will be very useful for all beginner researchers.
Clausius' formulation of the second law of thermodynamics, also known as the Clausius principle, states that a process that involves no changes except for the transfer of heat from a warmer body to a colder body is irreversible, i.e., heat cannot spontaneously pass from a colder body to a warmer one [7--10].
Clausius introduced the concept of entropy (S), a function of state of a system (a function that has a full differential). According to the Clausius inequality,
dS δQ / T, (1)
where the equality sign pertains to reversible processes and the inequality (greater-than) sign, to irreversible ones.
Expression (1) is suitable for a simple isolated system, which can exchange neither substance nor energy with the environment and whose internal energy (U) and volume (V) are constant. In such systems only the work of expansion or no work at all is performed. In this case, the second law of thermodynamics may be written as
dS 0 .
Thus, the entropy of this system increases when irreversible processes occur, and it is maximum in the state of thermodynamic equilibrium.
The second law of thermodynamics according to Thomson (Thomson's principle) states that the process during which work is transformed into heat without any other changes in the system's state is irreversible. This means that all heat withdrawn from a body cannot be entirely transformed into work unless the system is changed in other respects. This formulation is equivalent to the statement that the perpetuum mobile of the second kind is impossible [7-10].
Carnot's theorem is also equivalent to the impossibility of the perpetuum mobile of the second kind. According to this theorem, no heat engine can have a higher efficiency than that of the Carnot cycle, η = (T1 — T2)/T1, which is determined only by the temperatures of the heater and the cooler (T1 and T2, respectively). Carnot's theorem lays the basis for the absolute temperature scale.
Sometimes, the second law of thermodynamics is formulated as the well-known C. Caratheodory's principle (1909).
In the kinetic theory of gases, the second law of thermodynamics is substantiated by Boltzmann's H theorem. Here, H is the Boltzmann H function (to be precise, functional) determined from the mean logarithm of the particle distribution function. The Boltzmann H function is proportional to the entropy of the perfect gas.
The physical meaning of entropy is revealed in statistical physics. Boltzmann demonstrated that the entropy is related to the logarithm of thermodynamic probability (W):
S = k ln W,
where k is the Boltzmann constant.
Note that the Boltzmann's substantiating the statistical basis of the second law of thermodynamics, as well as the statistical substantiation of phenomenological thermodynamics suggested by Gibbs, involves ideal models, e.g., the perfect gas. In the case of more complex systems [3—4, 8], where pronounced (especially, strong) interactions between particles (molecules) are observed, it is difficult to perform the calculations. Therefore, it is obvious that these models are unlikely to be effective when studying most natural systems (e.g., biological), i.e., the systems that are far from corresponding to ideal or simple models.
The thermodynamics of nonequilibrium processes deals with the rate of increase in or (which is the same) production of entropy. Therefore, it is sometimes asserted that nonequilibrium thermodynamics provides "the quantitative characteristic of the second law of thermodynamics" [7]. In the given case, however, this statement is reasonable only when applied to transformations in simple isolated systems where all processes are close to equilibrium. Only in a system that is close to equilibrium can the differential of this function of state of the system (entropy) be considered to be a full one, to an acceptable approximation. However, all the aforesaid is usually underestimated; therefore, many works on nonequilibrium thermodynamics, especially the thermodynamics of systems that are far from equilibrium, remain a faint "future hope." Some of these works, I daresay, are mere "mathematically trimmed" fantasies useless for real life [22—24].
Historically, the formulations of the second law of thermodynamics were closely associated with the study of heat engines. This approach has been developed by physicists, mainly thermal physicists, and heat engineers. Another trend in the use of the second law of thermodynamics is related to the attempts of some mathematicians and physicists constructing ideal and simple models to explain many natural phenomena in statistical terms. However, since all interactions in real systems are impossible to take into account, there is but little hope that calculations in the framework of these models will successfully solve the problem. Hence, only the phenomenological thermodynamics of systems close to equilibrium (equilibrium or quasi-equilibrium thermodynamics) is likely to ensure the insight into many natural phenomena and make reliable quantitative predictions.
The above formulations of the second law of thermodynamics are, in a sense, somewhat outside the realm of the chemistry of molecular and supramolecular systems. These formulations may seem to be even farther from biology, sociology, and other sciences that are mainly based on chemistry (both molecular chemistry per se and the chemistry of supramolecular structures), which we perceive as "chemistry around us." Therefore, it is not unexpected that a purely physical (rather than physicochemical) approach to the origin of life, biological evolution, and aging of living organisms has lead to numerous misunderstandingsone might say, even to tragic errorsin life science. It should suffice to mention L. Boltzmann's, E. Schrdinger's, I. Progogine's [29—31], and other researchers' fallacies accounted for by neglecting (to some or another extent) Gibbs's works and underestimating the possibilities offered by thermodynamics. In some of my publications, I emphasized the substantial misunderstandings in this field [11, 20, 22, 23] that the founders of classical thermodynamics noted long ago [1, 2, 10—13].
To justify these statements, let me make a digression to cite the renowned scientists Boltzmann and Schrdinger [31] who asserted that living organisms struggle for negative entropy (also called negentropy). I will also cite some Prigogine's [29] quotations that appeared even on the cover of his books. The reader will find references to them in the Internet [31, 32].
I would like to note that the quotations presented below do not pertain to the second law of thermodynamics in its classical form [2, 9, 10]. Today, they may seem surprising, especially taking into account that all this was written several years after Gibbs published his works.
For example, Boltzmann (1886) wrote,
"The general struggle for existence of animate beings is therefore not a struggle for raw materials - these, for organisms, are air, water and soil, all abundantly availablenor for energy which exists in plenty in any body in the form of heat (albeit unfortunately not transformable), but a struggle for entropy, which becomes available through the transition of energy from the hot sun to the cold earth.".
Then, in 1944, Schrdinger wrote that "the only way a living system stays alive, away from maximum entropy or death is to be continually drawing from its environment negative entropy. Thus the device by which an organism maintains itself stationary at a fairly high level of orderliness (= fairly low level of entropy) really consists in continually sucking orderliness from its environment. Plants of course have their most powerful supply in negative entropy in sunlight".
Later, Prigogine also supposed (on the basis of previous notions of Boltzmann, Schrdinger, and their followers in life science) that the phenomenon of life is hardly consistent with the second law of thermodynamics. He noted, "During the last decades, an opinion has widely spread that there is the apparent contradiction between biological order and laws of physicsparticularly the second law of thermodynamics" (1980). Prigogine also emphasized that "this contradiction cannot be removed as long as one tries to understand living systems by the methods of equilibrium thermodynamics".
It order to solve these "contradictions", Prigogine [29] developed the theory of dissipative structures, i.e., the structures that appearing in systems that are far from equilibrium. Later, it turned out that the theory did not allow overcoming the aforementioned "contradictions." In fact, it made the imbroglio even more intricate. It later became obvious that Prigogine's views do not agree with the second law of thermodynamics [20, 22, 24]. This is so in many respects. Suffice it to say that, in the general case, the Prigogine entropy (S' or S ) has no full differential. Therefore, his theory cannot be regarded as thermodynamic. This is a kinetic theory based on an "entropy" (Prigogine's entropy, S') which can be neither calculated nor measured.
Prigogine considered Gibbs's work to be mainly theoretical and stated that Gibbs's method is inapplicable to studying physicochemical transformations, such as chemical reactions, because the values used in this method are the functions of state pertaining to the whole system or its individual component. Prigogine actively publicized his views via scientific literature and textbooks [30]. As a result, many researchers refer to Prigogine's formulation of the second law of thermodynamics. Actually, this formulation applies to a particular speculative model and may be accepted only on certain premises that cannot be proved. Unfortunately, this concept, which, in a sense, contradicts the principles of science itself [5, 6], was supported by many researchers. Owing to efficient publicity, these colleagues were convinced by hardly comprehensible (in physical terms) formulas and doubtful argumentation. In my opinion, the supporters of Prigogine's theory were, in a sense, deceived. Although Prigogine's theory proved an impasse, it still has its followers. Nevertheless, no numerical data obtained from either experiment or observation have confirmed the theory even at the qualitative level [20, 22]. Moreover, many physicochemical processes of the formation of spatially periodic structures (which Prigogine and his coauthors regarded as dissipative) were explained long ago in terms of the thermodynamic models of quasi-equilibrium systems (without involving the concept of dissipative structures). It is generally known that W.Ostwald (1897) used the notion of supersaturation to explain the existence of such systems in nature.
The Second Law of Thermodynamics and Evolution
of Living Systems
Georgi P. Gladyshev
International Academy of Creative Endeavors, San Diego, USA
Corresponding address: N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, Kosygina 4, Moscow, 117977, Russia
Abstract: The classical formulations of the second law of thermodynamics are presented. Some mistakes in the understanding the physical meaning of this general law of nature are noted. It is asserted that many misunderstandings of the second law of thermodynamics are related to terminological confusion and the underestimation of the theory developed by J.W. Gibbs and other founders of "true thermodynamics," which is impossible to disprove. To a certain approximation, R. Clausius and J.W. Gibbs' thermodynamics is applied to describing the evolution of living systems. This is possible due to the law of temporal hierarchies and the premise that the functions of state of living systems have real physical meaning at practically all hierarchical levels and at every moment of time. Making no pretensions to perfection, the author offers some advice to researchers dealing with thermodynamics. The author believes that, when considering thermodynamic problems, "ambiguous" terms and definitions should be clarified preliminarily in order to preclude possible misunderstandings. It is also advisable to refer to the classical works (including textbooks and encyclopedias) that the authors of publications have used. This will allow the correctness of the results reported to be estimated at least preliminarily.
Keywords: Second law, thermodynamics, chemical thermodynamics, entropy, Gibbs function, Gibbs energy, full differential, law of temporal hierarchies, evolution, living systems, quasi-closed systems.
AMS Mathematical Subject Classification: 74A15, 80-06, 80A50
PACS: 05.70.-a, 64, 82.60.-s, 95.30.Tg
" the true and only goal of science is
to reveal unity rather than mechanisms"
Henri Poincar
Classics of science actually enunciated the second law of thermodynamics, one of general laws of nature, in the first half of the 19th century. Well-known formulations of this law are associated with the names of N.L.S. Carnot (1824), R. Clausius, (1850), and W. Thomson (Lord Kelvin) (1851). Although the formulations themselves are different, mainly because of the difference in phrasing, they may be considered equivalent. Many authors have attempted to change or improve the formulations as regards their physical meaning, yet none has succeeded. The meaning (essence) of these formulations has not been disproved to date [1—23]. However, new concepts have extended the possible applications of the second law of thermodynamics to different sciences, especially chemistry and, as it turned out later, biology. This became possible mainly due to J.W. Gibbs' works performed in 1873—1878. To a certain approximation, the methodology of Gibbs thermodynamics [2] has been extended to date to all hierarchies of natural systems, which are generally open ones [17]. The discovery of the law of temporal hierarchies, which may be considered a new general law of nature, has determined the extension of Gibbs's theory to living systems [17, 22—28]. This law [17] makes it possible to apply thermodynamics (more precisely, the hierarchic thermodynamics of quasi-closed systems), to all hierarchies of the real world, particularly, living objects and biological systems, to quite a good approximation. I believe that the discovery of this law confirms the universality of classical thermodynamic methods, and the name of Josiah Willard Gibbs even more vividly symbolizes the future of science that confirms the validity of general laws of nature as applied to the evolution of all material systems at all organizational levels of our world. Advances in classical thermodynamics (as well as approximate thermodynamics, i.e., the quasi-equilibrium thermodynamics of quasi-closed systems) are described in a number of textbooks and monographs. They are certainly numerous; I would especially recommend the works [1—17], which will be very useful for all beginner researchers.
Clausius' formulation of the second law of thermodynamics, also known as the Clausius principle, states that a process that involves no changes except for the transfer of heat from a warmer body to a colder body is irreversible, i.e., heat cannot spontaneously pass from a colder body to a warmer one [7--10].
Clausius introduced the concept of entropy (S), a function of state of a system (a function that has a full differential). According to the Clausius inequality,
dS δQ / T, (1)
where the equality sign pertains to reversible processes and the inequality (greater-than) sign, to irreversible ones.
Expression (1) is suitable for a simple isolated system, which can exchange neither substance nor energy with the environment and whose internal energy (U) and volume (V) are constant. In such systems only the work of expansion or no work at all is performed. In this case, the second law of thermodynamics may be written as
dS 0 .
Thus, the entropy of this system increases when irreversible processes occur, and it is maximum in the state of thermodynamic equilibrium.
The second law of thermodynamics according to Thomson (Thomson's principle) states that the process during which work is transformed into heat without any other changes in the system's state is irreversible. This means that all heat withdrawn from a body cannot be entirely transformed into work unless the system is changed in other respects. This formulation is equivalent to the statement that the perpetuum mobile of the second kind is impossible [7-10].
Carnot's theorem is also equivalent to the impossibility of the perpetuum mobile of the second kind. According to this theorem, no heat engine can have a higher efficiency than that of the Carnot cycle, η = (T1 — T2)/T1, which is determined only by the temperatures of the heater and the cooler (T1 and T2, respectively). Carnot's theorem lays the basis for the absolute temperature scale.
Sometimes, the second law of thermodynamics is formulated as the well-known C. Caratheodory's principle (1909).
In the kinetic theory of gases, the second law of thermodynamics is substantiated by Boltzmann's H theorem. Here, H is the Boltzmann H function (to be precise, functional) determined from the mean logarithm of the particle distribution function. The Boltzmann H function is proportional to the entropy of the perfect gas.
The physical meaning of entropy is revealed in statistical physics. Boltzmann demonstrated that the entropy is related to the logarithm of thermodynamic probability (W):
S = k ln W,
where k is the Boltzmann constant.
Note that the Boltzmann's substantiating the statistical basis of the second law of thermodynamics, as well as the statistical substantiation of phenomenological thermodynamics suggested by Gibbs, involves ideal models, e.g., the perfect gas. In the case of more complex systems [3—4, 8], where pronounced (especially, strong) interactions between particles (molecules) are observed, it is difficult to perform the calculations. Therefore, it is obvious that these models are unlikely to be effective when studying most natural systems (e.g., biological), i.e., the systems that are far from corresponding to ideal or simple models.
The thermodynamics of nonequilibrium processes deals with the rate of increase in or (which is the same) production of entropy. Therefore, it is sometimes asserted that nonequilibrium thermodynamics provides "the quantitative characteristic of the second law of thermodynamics" [7]. In the given case, however, this statement is reasonable only when applied to transformations in simple isolated systems where all processes are close to equilibrium. Only in a system that is close to equilibrium can the differential of this function of state of the system (entropy) be considered to be a full one, to an acceptable approximation. However, all the aforesaid is usually underestimated; therefore, many works on nonequilibrium thermodynamics, especially the thermodynamics of systems that are far from equilibrium, remain a faint "future hope." Some of these works, I daresay, are mere "mathematically trimmed" fantasies useless for real life [22—24].
Historically, the formulations of the second law of thermodynamics were closely associated with the study of heat engines. This approach has been developed by physicists, mainly thermal physicists, and heat engineers. Another trend in the use of the second law of thermodynamics is related to the attempts of some mathematicians and physicists constructing ideal and simple models to explain many natural phenomena in statistical terms. However, since all interactions in real systems are impossible to take into account, there is but little hope that calculations in the framework of these models will successfully solve the problem. Hence, only the phenomenological thermodynamics of systems close to equilibrium (equilibrium or quasi-equilibrium thermodynamics) is likely to ensure the insight into many natural phenomena and make reliable quantitative predictions.
The above formulations of the second law of thermodynamics are, in a sense, somewhat outside the realm of the chemistry of molecular and supramolecular systems. These formulations may seem to be even farther from biology, sociology, and other sciences that are mainly based on chemistry (both molecular chemistry per se and the chemistry of supramolecular structures), which we perceive as "chemistry around us." Therefore, it is not unexpected that a purely physical (rather than physicochemical) approach to the origin of life, biological evolution, and aging of living organisms has lead to numerous misunderstandingsone might say, even to tragic errorsin life science. It should suffice to mention L. Boltzmann's, E. Schrdinger's, I. Progogine's [29—31], and other researchers' fallacies accounted for by neglecting (to some or another extent) Gibbs's works and underestimating the possibilities offered by thermodynamics. In some of my publications, I emphasized the substantial misunderstandings in this field [11, 20, 22, 23] that the founders of classical thermodynamics noted long ago [1, 2, 10—13].
To justify these statements, let me make a digression to cite the renowned scientists Boltzmann and Schrdinger [31] who asserted that living organisms struggle for negative entropy (also called negentropy). I will also cite some Prigogine's [29] quotations that appeared even on the cover of his books. The reader will find references to them in the Internet [31, 32].
I would like to note that the quotations presented below do not pertain to the second law of thermodynamics in its classical form [2, 9, 10]. Today, they may seem surprising, especially taking into account that all this was written several years after Gibbs published his works.
For example, Boltzmann (1886) wrote,
"The general struggle for existence of animate beings is therefore not a struggle for raw materials - these, for organisms, are air, water and soil, all abundantly availablenor for energy which exists in plenty in any body in the form of heat (albeit unfortunately not transformable), but a struggle for entropy, which becomes available through the transition of energy from the hot sun to the cold earth.".
Then, in 1944, Schrdinger wrote that "the only way a living system stays alive, away from maximum entropy or death is to be continually drawing from its environment negative entropy. Thus the device by which an organism maintains itself stationary at a fairly high level of orderliness (= fairly low level of entropy) really consists in continually sucking orderliness from its environment. Plants of course have their most powerful supply in negative entropy in sunlight".
Later, Prigogine also supposed (on the basis of previous notions of Boltzmann, Schrdinger, and their followers in life science) that the phenomenon of life is hardly consistent with the second law of thermodynamics. He noted, "During the last decades, an opinion has widely spread that there is the apparent contradiction between biological order and laws of physicsparticularly the second law of thermodynamics" (1980). Prigogine also emphasized that "this contradiction cannot be removed as long as one tries to understand living systems by the methods of equilibrium thermodynamics".
It order to solve these "contradictions", Prigogine [29] developed the theory of dissipative structures, i.e., the structures that appearing in systems that are far from equilibrium. Later, it turned out that the theory did not allow overcoming the aforementioned "contradictions." In fact, it made the imbroglio even more intricate. It later became obvious that Prigogine's views do not agree with the second law of thermodynamics [20, 22, 24]. This is so in many respects. Suffice it to say that, in the general case, the Prigogine entropy (S' or S ) has no full differential. Therefore, his theory cannot be regarded as thermodynamic. This is a kinetic theory based on an "entropy" (Prigogine's entropy, S') which can be neither calculated nor measured.
Prigogine considered Gibbs's work to be mainly theoretical and stated that Gibbs's method is inapplicable to studying physicochemical transformations, such as chemical reactions, because the values used in this method are the functions of state pertaining to the whole system or its individual component. Prigogine actively publicized his views via scientific literature and textbooks [30]. As a result, many researchers refer to Prigogine's formulation of the second law of thermodynamics. Actually, this formulation applies to a particular speculative model and may be accepted only on certain premises that cannot be proved. Unfortunately, this concept, which, in a sense, contradicts the principles of science itself [5, 6], was supported by many researchers. Owing to efficient publicity, these colleagues were convinced by hardly comprehensible (in physical terms) formulas and doubtful argumentation. In my opinion, the supporters of Prigogine's theory were, in a sense, deceived. Although Prigogine's theory proved an impasse, it still has its followers. Nevertheless, no numerical data obtained from either experiment or observation have confirmed the theory even at the qualitative level [20, 22]. Moreover, many physicochemical processes of the formation of spatially periodic structures (which Prigogine and his coauthors regarded as dissipative) were explained long ago in terms of the thermodynamic models of quasi-equilibrium systems (without involving the concept of dissipative structures). It is generally known that W.Ostwald (1897) used the notion of supersaturation to explain the existence of such systems in nature.
Thus, the aforementioned concepts by Boltzmann, Schrdinger, Prigogine, and their followers turned out to be at best tentative ones, or even a dead end. They hampered for many decades the search for the ways to explaining the evolution of living systems in physicochemical terms on the basis of the second law of thermodynamics. As noted above, only in recent decades were the principles of hierarchical thermodynamics (macrothermodynamics) formulated. I have managed to extend Gibbs's methodology so that it might be used for creating the physical (physicochemical) theories of the origin of life, biological evolution, and aging of living organisms [17, 22—28].
As noted above, the physical substantiation of the second law of thermodynamics deals with ideal processes and is based on the concept of statistical entropy. The nonequilibrium thermodynamics of systems that are far from equilibrium tries to study the changes in "kinetic entropy" (e.g., Prigogine's entropy S' or (S' or S ), which, as mentioned above, has no full differential (even an approximate one) and cannot be calculated in principle! In addition, the approaches used in the nonequilibrium thermodynamics of systems far from equilibrium create difficulties related, e.g., to the notions on the thermodynamics of processes and the thermodynamics of systems.
One of the greatest merits of Gibbs and other renowned founders of classical thermodynamics is that they used the works by J.L. Lagrange, L. Euler, and other outstanding mathematicians (specifically, the variation principles developed by them) as a basis for the concepts on the functions of state of the system other than entropy (which, like entropy, have full differentials). The functions of state permit determining the directions of spontaneous processes and estimating the extent of their advancement in individual thermodynamic systems identified in the real world. In other words, the evolution of systems themselves can now be studied, to a certain approximation, if certain natural (independent) variables are constant. The Gibbs function G (the Gibbs free energy or, more briefly, the Gibbs energy) can be used for studying equilibrium (quasi-equilibrium) processes and closed systems (the quasi-closed systems in which quasi-equilibrium transformations occur) at constant temperature and pressure. The Helmholtz function F (A) is applicable to studying these processes and systems at constant temperature and volume. Certainly, this is only true on the assumption that the functions of state (of the systems studied) have actual physical sense at any moment of time. This is true for systems close to equilibrium but not for those far from equilibrium. I would like to emphasize once more that the law of temporal hierarchies gives grounds for the use of the functions of state when the direction and the extent of advancement of the evolutionary processes that occur in quasi-closed systems are estimated at different hierarchical levels of living matter [17]. For clarity, let us make a digression on the law of temporal hierarchies.
The law of temporal hierarchies makes it possible to identify quasi-closed thermodynamic systems (subsystems) within open biological systems and to study the individual development (ontogenesis) and evolution (phylogenesis) of these subsystems via studying the changes in the specific (calculated per unit volume or mass) Gibbs function for the formation of a given higher monohierarchical structure out of lower monohierarchical structures. For example, it has been found that the specific Gibbs function for the formation of supramolecular structures of biological tissues ( ) tends towards its minimum in the course of ontogenesis (as well as phylogenesis and evolution as a whole):
, (2)
where V is the volume of the system, m is the mass of the microvolumes identified, x, y, and z are coordinates, the symbol - means that is a specific value (i.e., calculated per unit macrovolume), and the symbol ~ emphasizes that the system is heterogeneous. Note that expression (2) implies that the intermolecular (supramolecular) interactions in all hierarchical structures of biological tissues (both intracellular and intercellular interactions) are taken into account. This is justified because the structural hierarchy does not necessarily coincide with the temporal one. For example, cells of some types do not divide; like organs, they age simultaneously with the body as a whole. However, for each supramolecular hierarchy (j—1), there exists a higher hierarchy (j+х) such that
<< ,
where and are the mean lifetimes (or lifespan) of the elementary structures of the respective structural hierarchies in the living system; х = 0, 1, 2, etc.
Note that the internal medium and many fragments of nondividing cells are nevertheless renewed due to metabolism.
The use of expression (2) actually means that, in the given case, the law of temporal hierarchies assumes the following form:
<< << << << << . (3)
Here, ( ) is the mean lifetime of molecules (chemical substance) involved in metabolism in the body, ( ) is the mean lifetime of all intermolecular (supramolecular) structures of tissues renewed during individual growth and development, is the mean lifetime of individual organisms in a population, and is the mean population lifetime. I have deliberately excluded the lifetimes of cells and some other complex supramolecular structures from the series of strong inequalities (3) for the reasons indicated above. However, this series certainly represents a general law of nature consistent with reality and reflecting the existence of temporal hierarchies in living systems.
The law of temporal hierarchies is related to the presence of metabolism or other forms of substance transformation at all hierarchical levels. Note that metabolism is an essential characteristic of living organisms.
This law (Gladyshev's law) allows strict demonstration of the possibility to identify (discern) quasi-open monohierarchical systems (subsystems) within open polyhierarchical biological systems. This statement entirely agrees with the experience accumulated in theoretical and experimental physics [3, 5]. I am convinced that this assertion cannot raise any objections.
It is impossible in this short article to list all important conditions for the use of some or another function of state of the system. Moreover, I do not think I have noted all of the main "delicate" points that beginners should take into account. Besides, I refer to just a few publications, those that are most important for me. It should also be noted that my paper, as well as most publications on thermodynamics, may contain some inaccuracies of wording resulting from the ambiguity of translation. For example, most professional scientists know about inexcusable confusions with the terms isolated system and closed system (originally English). Both terms are sometimes translated into Russian as замкнутая система (literally, closed system). So the terms are often regarded as equivalent or identical. Other errors result from semantic coincidence of some terms. For example, the Gibbs (or Helmholtz) free energy is often confused with energy in the ordinary sense. This is why many researchers have attempted to replace this term with the term the Gibbs function [19]. Another example is the term complex system. Here, the word complex has a double meaning. In thermodynamics, a complex system (as opposed to a simple one) usually means a system in which (or on which) a work other than the work of expansion is done [15, 16]. Sometimes, however, the word complex is used to emphasize a structural or some other heterogeneity of the system itself or the diversity of its elements. This also applies to the term simple system, and so on. Certainly, these and other such confusions may lead to blunders that escape a nonprofessional's notice. These and other similar errors creep into some textbooks, reference books, and then into the Internet. I presume the possible inaccuracy of my English in this paper is insignificant, and I hope that the above remarks will warn beginners about the erroneous views that may exist in thermodynamics. I think that all physicists, chemists, biologists, and other specialists that deal with thermodynamics should study the Gibbs phenomenological thermodynamics first of all. As noted above, this authentic (in a certain sense, true) thermodynamics is based on the notion of full differentials. Note that this approach to understanding the world surrounding us is intrinsically irrefutable. We may only discuss the accuracy of the Gibbs thermodynamics as applied to, e.g., quasi-closed systems the processes in which are close to equilibrium. In accord with the very essence of full differential (its mathematical meaning), as well as the first law of thermodynamics, the change in the function of state of the system accompanying the transition from one equilibrium state to another is independent of the way or mechanisms of this transition. Probably, the lack of our knowledge on actual complex systems may be partly attributed to the changes in entropy during this transition, because the entropy cannot be measured directly. The changes in phenomenological entropy accompanying transformations in both simple and complex systems may be calculated only if one has studied the corresponding thermal processes. In statistical terms, the entropy is calculated only for ideal systems (or systems close to ideal). It is impossible to perform any precise calculations of this function of state for systems with strong interactions between particles (molecules and supramolecular structures) on a statistical basis. I would like to emphasize that this applies to complex thermodynamic systems, i.e., the systems in which strong interactions occur.
Thermodynamics, owing to its impeccably reliable mathematical basis, may be regarded as a "machine" that always yields the right result if the premises are correct. Physical chemistry has repeatedly confirmed this [8—10, 14, 19]. Unfortunately, some physicists, biophysicists, biologists, and, especially, modern "philosophers" are still unaware of this experience of chemists and chemical technologists.
I would like to repeat that the aforementioned ambiguities, which are mainly related to the underestimation of the correct use of many terms that are semantically similar but differ in physical meaning, result in confusion and misunderstandings. These misunderstandings discredit, at least in nonprofessionals' opinion, thermodynamics itself and science as a whole. Hence the numerous incorrect interpretations of the second law of thermodynamics, various dubious "views" on entropy [11, 13, 20, 22], and far-fetched "the functions of state of the system." Many authors, ignoring classical works in this field, apply different formulations of the second law of thermodynamics to systems where they are inherently inapplicable. Some of these authors suggest their own interpretations of this general law of nature. This debases science and education. Moreover, it can be said that several "second laws of thermodynamics" have appeared, none of which having anything to do with reality. A good example is the aforementioned Prigogine's [29] interpretation of the second law of thermodynamics. This interpretation "extends" the well-known incorrect and indemonstrable statement by the great Boltzmann [31], who underestimated the important concepts put forward by Clausius and Gibbs. The interpretation suggested by Prigogine has practically conquered the "scientific" world and still remains one of the trendiest interpretations of the second law of thermodynamics. I am well aware that it would be hopeless to argue with the visionaries that create or support these concepts: they have developed an excellent method for leading such debates. They unfailingly give lots of arguments, which are mostly quotations from published or oral statements made by other visionaries or by insufficiently informed scientists. It is often emphasized that those scientists are well known or even famous. However, the visionaries forget that scientists that are well known and famous in one field are not necessarily professionals in others. The only way to withstand this conjuncture is to refer the readers to classical works and serious textbooks written in a highly professional milieu of world-renowned scientific schools with centuries-long traditions.
Thus, making no pretensions to perfection, I would like nevertheless to offer advice to researchers dealing with thermodynamics, as well as other branches of science, and the editors of scientific periodicals. My advice is the following. When discussing the problems of thermodynamics or using its mathematical tools for calculations, it is necessary to clarify "ambiguous" terms and definitions. It is also advisable to refer to the classical works (including textbooks, reference books, and encyclopedias) that the authors of publications used. In this case, the correctness of the results reported in the publications can be at least preliminarily estimated.
I am grateful to Prof. M.M. Abdildin, Prof. G. Arrhenius, Prof. N.N. Bogolyubov, Jr., Prof. K.G. Denbigh, Prof. V.P. Kazakov, Prof. Yu.S. Lipatov, Prof. A.A. Logunov, Prof. V.V. Sychev, and Prof. V.M. Frolov for the support, systematic fruitful discussions, and valuable advice.
Conclusion
To a certain approximation, R. Clausius and J.W. Gibbs' thermodynamics is applied to describing the evolution of living systems. This is possible due to the law of temporal hierarchies and the premise that the functions of state of living systems have real physical meaning at practically all hierarchical levels and at every moment of time. The author believes that, when considering thermodynamic problems, "ambiguous" terms and definitions should be clarified preliminarily in order to preclude possible misunderstandings. It is also advisable to refer to the classical works (including textbooks and encyclopedias) that the authors of publications have used.
References
1. A. Poincare’, On Science; Nauka: Moscow, 1983, 560 p.
2. J.W. Gibbs, The Collected Works of J. Willard Gibbs. Thermodynamics; Longmans, Green and Co.: New York, 1928, V. 1, pp 55-349.
3. N.N. Bogolubov, Selected works. Part 1, Dynamical Theory; Gordon and Breach Science Publishers: New York, 1990.
4. N.N. Bogolubov and N.N. Bogolubov, Jr., An Introduction to Quantum Statistical mechanics; Gordon and Breach Science publishers: Library of Congress Catalog ISBN, 2-88124-879-9, QC 174.4.B6413 , 1992.
5. L.I. Sedov, The Thoughts on Science and on Scientists; Nauka, Russian Academy of Sciences, V.A. Steklov Mathematical Institute: Moscow, 1980, 440 p.
6. L.I. Sedov, Priroda - Russ., 1984, 11, 3.
7. D.N. Zubarev, The Carnot theorem, Physical Encyclopedia - Soviet Encyclopedia: Moscow, 1990; Vol. , pp. 242-243.
8. R.A Alberty, Physical Chemistry, 7th Ed.; Wiley: New York, Etc., 1987, 934 p.
9. R.J. Silbey, R.A Alberty, Physical Chemistry, 3rd Ed.; John Wiley & Sons: New York, 2001.
10. K.G. Denbigh, The Principle of Chemical Equilibrium, 3ed Ed.; Cambridge Univ. Press: Cambridge, 1971, 491 p.
11. K.G. Denbigh, Brit. J. Phyl. Sci. 1989, 40, 323.
12. K.G. Denbigh, Brit. J. Phil Sci. 1989, 40, 501.
13. K.G. Denbigh, J.S. Denbigh, Entropy in Relation to Incomplete Knowledge; Cambridge University Press: Cambridge, 1985.
14. Ch.R. Cantor, P.R. Schimmel, Biophysical Chemistry; Mir: Moscow, 1984-1985; Vol. 1-3.
15. V.V. Sychev, Thermodynamics of Complex Systems ; Energoatomizdat: Moscow, 1986, 208 p.
16. V.V. Sychev, Differential Equations of Thermodynamics ; Nauka: Moscow, 1981, 195 p.
17. G.P. Gladyshev, Supramolecular thermodynamics is a key to understanding phenomenon of life. What is Life from a Physical Chemist’s Viewpoint; Second Ed.; Regular and Chaotic Dynamics: Moscow — Izhevsk, 2003, 144 p. (In Russian).
18. Yu.S. Lipatov, Phase-Separated Interpenetrating Polymer Networks; USChTU (ISBN 966-8018-12) : Dnepropetrovsk, 2001, 326p.
19. M.N. Jones, Ed., Biochemical Thermodynamics; Elsevier Scientific Publishing Company: Amsterdam — Oxford — New York, 1979 (Russian translation. Mir: Moscow, 1982, 440 p.).
20. Shu-Kun Lin, Entropy, 1999, 1, 1 -
http://www.mdpi.org/entropy21. R.A. Alberty, Research Summary; Massachusetts Institute of Technology, Chemistry : Internet, 2004
MIT Department of Chemistry – Department of Chemistry at MIT22. G.P. Gladyshev, International Journal of Modern Physics B, 2004, 18, 6, 801.
23 G.P. Gladyshev, Progress in Reaction Kinetics and Mechanism (An International Review Journal), 2003, 28, 157.
24. G.P. Gladyshev, Proceedings of International Higher Education Academy of Sciences, 2003, 4 (26), 19.
25. G.P. Gladyshev, Electron. J. Math. Phys. Sci., 2002, Sem. 2, 1
http://www.ejmaps.org26. G.P. Gladyshev, SEED Journal (Canada), 2002, 3, 42,
Error 404 | University of Toronto Libraries27. G.P. Gladyshev, Entropy, 1999, 1, 2, 9
http://www.mdpi.org/entropy28. G.P. Gladyshev, Entropy, 1999, 1, 4, 55
http://www.mdpi.org/entropy29. I. Prigogine, From Being to Becoming: Time and Complexity and the Physical Sciences; W.H. Freeman & Co.: San Francisco, 1980.
30. I. Prigogine, R.Defey, Chemical Thermodynamics; Nauka: Novosibirsk, 1966, 509p.
31. References of works of L.Boltzmann, E.Schrdinger end I.Prigogine one can find in web-page
http://www.redfish.com/...eiderKay1995_OrderFromDisorder.htm(E.D. Schneider, J.J. Kay, 1995, "Order from Disorder: The Thermodynamics of Complexity in Biology", in Michael P. Murphy, Luke A.J. O'Neill (ed), "What is Life: The Next Fifty Years. Reflections on the Future of Biology"; Cambridge University Press, pp. 161-172).
32. Information in Internet, The problems of Thermodynamics of Biological Evolution
http://www.endeav.org/evolut
As noted above, the physical substantiation of the second law of thermodynamics deals with ideal processes and is based on the concept of statistical entropy. The nonequilibrium thermodynamics of systems that are far from equilibrium tries to study the changes in "kinetic entropy" (e.g., Prigogine's entropy S' or (S' or S ), which, as mentioned above, has no full differential (even an approximate one) and cannot be calculated in principle! In addition, the approaches used in the nonequilibrium thermodynamics of systems far from equilibrium create difficulties related, e.g., to the notions on the thermodynamics of processes and the thermodynamics of systems.
One of the greatest merits of Gibbs and other renowned founders of classical thermodynamics is that they used the works by J.L. Lagrange, L. Euler, and other outstanding mathematicians (specifically, the variation principles developed by them) as a basis for the concepts on the functions of state of the system other than entropy (which, like entropy, have full differentials). The functions of state permit determining the directions of spontaneous processes and estimating the extent of their advancement in individual thermodynamic systems identified in the real world. In other words, the evolution of systems themselves can now be studied, to a certain approximation, if certain natural (independent) variables are constant. The Gibbs function G (the Gibbs free energy or, more briefly, the Gibbs energy) can be used for studying equilibrium (quasi-equilibrium) processes and closed systems (the quasi-closed systems in which quasi-equilibrium transformations occur) at constant temperature and pressure. The Helmholtz function F (A) is applicable to studying these processes and systems at constant temperature and volume. Certainly, this is only true on the assumption that the functions of state (of the systems studied) have actual physical sense at any moment of time. This is true for systems close to equilibrium but not for those far from equilibrium. I would like to emphasize once more that the law of temporal hierarchies gives grounds for the use of the functions of state when the direction and the extent of advancement of the evolutionary processes that occur in quasi-closed systems are estimated at different hierarchical levels of living matter [17]. For clarity, let us make a digression on the law of temporal hierarchies.
The law of temporal hierarchies makes it possible to identify quasi-closed thermodynamic systems (subsystems) within open biological systems and to study the individual development (ontogenesis) and evolution (phylogenesis) of these subsystems via studying the changes in the specific (calculated per unit volume or mass) Gibbs function for the formation of a given higher monohierarchical structure out of lower monohierarchical structures. For example, it has been found that the specific Gibbs function for the formation of supramolecular structures of biological tissues ( ) tends towards its minimum in the course of ontogenesis (as well as phylogenesis and evolution as a whole):
, (2)
where V is the volume of the system, m is the mass of the microvolumes identified, x, y, and z are coordinates, the symbol - means that is a specific value (i.e., calculated per unit macrovolume), and the symbol ~ emphasizes that the system is heterogeneous. Note that expression (2) implies that the intermolecular (supramolecular) interactions in all hierarchical structures of biological tissues (both intracellular and intercellular interactions) are taken into account. This is justified because the structural hierarchy does not necessarily coincide with the temporal one. For example, cells of some types do not divide; like organs, they age simultaneously with the body as a whole. However, for each supramolecular hierarchy (j—1), there exists a higher hierarchy (j+х) such that
<< ,
where and are the mean lifetimes (or lifespan) of the elementary structures of the respective structural hierarchies in the living system; х = 0, 1, 2, etc.
Note that the internal medium and many fragments of nondividing cells are nevertheless renewed due to metabolism.
The use of expression (2) actually means that, in the given case, the law of temporal hierarchies assumes the following form:
<< << << << << . (3)
Here, ( ) is the mean lifetime of molecules (chemical substance) involved in metabolism in the body, ( ) is the mean lifetime of all intermolecular (supramolecular) structures of tissues renewed during individual growth and development, is the mean lifetime of individual organisms in a population, and is the mean population lifetime. I have deliberately excluded the lifetimes of cells and some other complex supramolecular structures from the series of strong inequalities (3) for the reasons indicated above. However, this series certainly represents a general law of nature consistent with reality and reflecting the existence of temporal hierarchies in living systems.
The law of temporal hierarchies is related to the presence of metabolism or other forms of substance transformation at all hierarchical levels. Note that metabolism is an essential characteristic of living organisms.
This law (Gladyshev's law) allows strict demonstration of the possibility to identify (discern) quasi-open monohierarchical systems (subsystems) within open polyhierarchical biological systems. This statement entirely agrees with the experience accumulated in theoretical and experimental physics [3, 5]. I am convinced that this assertion cannot raise any objections.
It is impossible in this short article to list all important conditions for the use of some or another function of state of the system. Moreover, I do not think I have noted all of the main "delicate" points that beginners should take into account. Besides, I refer to just a few publications, those that are most important for me. It should also be noted that my paper, as well as most publications on thermodynamics, may contain some inaccuracies of wording resulting from the ambiguity of translation. For example, most professional scientists know about inexcusable confusions with the terms isolated system and closed system (originally English). Both terms are sometimes translated into Russian as замкнутая система (literally, closed system). So the terms are often regarded as equivalent or identical. Other errors result from semantic coincidence of some terms. For example, the Gibbs (or Helmholtz) free energy is often confused with energy in the ordinary sense. This is why many researchers have attempted to replace this term with the term the Gibbs function [19]. Another example is the term complex system. Here, the word complex has a double meaning. In thermodynamics, a complex system (as opposed to a simple one) usually means a system in which (or on which) a work other than the work of expansion is done [15, 16]. Sometimes, however, the word complex is used to emphasize a structural or some other heterogeneity of the system itself or the diversity of its elements. This also applies to the term simple system, and so on. Certainly, these and other such confusions may lead to blunders that escape a nonprofessional's notice. These and other similar errors creep into some textbooks, reference books, and then into the Internet. I presume the possible inaccuracy of my English in this paper is insignificant, and I hope that the above remarks will warn beginners about the erroneous views that may exist in thermodynamics. I think that all physicists, chemists, biologists, and other specialists that deal with thermodynamics should study the Gibbs phenomenological thermodynamics first of all. As noted above, this authentic (in a certain sense, true) thermodynamics is based on the notion of full differentials. Note that this approach to understanding the world surrounding us is intrinsically irrefutable. We may only discuss the accuracy of the Gibbs thermodynamics as applied to, e.g., quasi-closed systems the processes in which are close to equilibrium. In accord with the very essence of full differential (its mathematical meaning), as well as the first law of thermodynamics, the change in the function of state of the system accompanying the transition from one equilibrium state to another is independent of the way or mechanisms of this transition. Probably, the lack of our knowledge on actual complex systems may be partly attributed to the changes in entropy during this transition, because the entropy cannot be measured directly. The changes in phenomenological entropy accompanying transformations in both simple and complex systems may be calculated only if one has studied the corresponding thermal processes. In statistical terms, the entropy is calculated only for ideal systems (or systems close to ideal). It is impossible to perform any precise calculations of this function of state for systems with strong interactions between particles (molecules and supramolecular structures) on a statistical basis. I would like to emphasize that this applies to complex thermodynamic systems, i.e., the systems in which strong interactions occur.
Thermodynamics, owing to its impeccably reliable mathematical basis, may be regarded as a "machine" that always yields the right result if the premises are correct. Physical chemistry has repeatedly confirmed this [8—10, 14, 19]. Unfortunately, some physicists, biophysicists, biologists, and, especially, modern "philosophers" are still unaware of this experience of chemists and chemical technologists.
I would like to repeat that the aforementioned ambiguities, which are mainly related to the underestimation of the correct use of many terms that are semantically similar but differ in physical meaning, result in confusion and misunderstandings. These misunderstandings discredit, at least in nonprofessionals' opinion, thermodynamics itself and science as a whole. Hence the numerous incorrect interpretations of the second law of thermodynamics, various dubious "views" on entropy [11, 13, 20, 22], and far-fetched "the functions of state of the system." Many authors, ignoring classical works in this field, apply different formulations of the second law of thermodynamics to systems where they are inherently inapplicable. Some of these authors suggest their own interpretations of this general law of nature. This debases science and education. Moreover, it can be said that several "second laws of thermodynamics" have appeared, none of which having anything to do with reality. A good example is the aforementioned Prigogine's [29] interpretation of the second law of thermodynamics. This interpretation "extends" the well-known incorrect and indemonstrable statement by the great Boltzmann [31], who underestimated the important concepts put forward by Clausius and Gibbs. The interpretation suggested by Prigogine has practically conquered the "scientific" world and still remains one of the trendiest interpretations of the second law of thermodynamics. I am well aware that it would be hopeless to argue with the visionaries that create or support these concepts: they have developed an excellent method for leading such debates. They unfailingly give lots of arguments, which are mostly quotations from published or oral statements made by other visionaries or by insufficiently informed scientists. It is often emphasized that those scientists are well known or even famous. However, the visionaries forget that scientists that are well known and famous in one field are not necessarily professionals in others. The only way to withstand this conjuncture is to refer the readers to classical works and serious textbooks written in a highly professional milieu of world-renowned scientific schools with centuries-long traditions.
Thus, making no pretensions to perfection, I would like nevertheless to offer advice to researchers dealing with thermodynamics, as well as other branches of science, and the editors of scientific periodicals. My advice is the following. When discussing the problems of thermodynamics or using its mathematical tools for calculations, it is necessary to clarify "ambiguous" terms and definitions. It is also advisable to refer to the classical works (including textbooks, reference books, and encyclopedias) that the authors of publications used. In this case, the correctness of the results reported in the publications can be at least preliminarily estimated.
I am grateful to Prof. M.M. Abdildin, Prof. G. Arrhenius, Prof. N.N. Bogolyubov, Jr., Prof. K.G. Denbigh, Prof. V.P. Kazakov, Prof. Yu.S. Lipatov, Prof. A.A. Logunov, Prof. V.V. Sychev, and Prof. V.M. Frolov for the support, systematic fruitful discussions, and valuable advice.
Conclusion
To a certain approximation, R. Clausius and J.W. Gibbs' thermodynamics is applied to describing the evolution of living systems. This is possible due to the law of temporal hierarchies and the premise that the functions of state of living systems have real physical meaning at practically all hierarchical levels and at every moment of time. The author believes that, when considering thermodynamic problems, "ambiguous" terms and definitions should be clarified preliminarily in order to preclude possible misunderstandings. It is also advisable to refer to the classical works (including textbooks and encyclopedias) that the authors of publications have used.
References
1. A. Poincare’, On Science; Nauka: Moscow, 1983, 560 p.
2. J.W. Gibbs, The Collected Works of J. Willard Gibbs. Thermodynamics; Longmans, Green and Co.: New York, 1928, V. 1, pp 55-349.
3. N.N. Bogolubov, Selected works. Part 1, Dynamical Theory; Gordon and Breach Science Publishers: New York, 1990.
4. N.N. Bogolubov and N.N. Bogolubov, Jr., An Introduction to Quantum Statistical mechanics; Gordon and Breach Science publishers: Library of Congress Catalog ISBN, 2-88124-879-9, QC 174.4.B6413 , 1992.
5. L.I. Sedov, The Thoughts on Science and on Scientists; Nauka, Russian Academy of Sciences, V.A. Steklov Mathematical Institute: Moscow, 1980, 440 p.
6. L.I. Sedov, Priroda - Russ., 1984, 11, 3.
7. D.N. Zubarev, The Carnot theorem, Physical Encyclopedia - Soviet Encyclopedia: Moscow, 1990; Vol. , pp. 242-243.
8. R.A Alberty, Physical Chemistry, 7th Ed.; Wiley: New York, Etc., 1987, 934 p.
9. R.J. Silbey, R.A Alberty, Physical Chemistry, 3rd Ed.; John Wiley & Sons: New York, 2001.
10. K.G. Denbigh, The Principle of Chemical Equilibrium, 3ed Ed.; Cambridge Univ. Press: Cambridge, 1971, 491 p.
11. K.G. Denbigh, Brit. J. Phyl. Sci. 1989, 40, 323.
12. K.G. Denbigh, Brit. J. Phil Sci. 1989, 40, 501.
13. K.G. Denbigh, J.S. Denbigh, Entropy in Relation to Incomplete Knowledge; Cambridge University Press: Cambridge, 1985.
14. Ch.R. Cantor, P.R. Schimmel, Biophysical Chemistry; Mir: Moscow, 1984-1985; Vol. 1-3.
15. V.V. Sychev, Thermodynamics of Complex Systems ; Energoatomizdat: Moscow, 1986, 208 p.
16. V.V. Sychev, Differential Equations of Thermodynamics ; Nauka: Moscow, 1981, 195 p.
17. G.P. Gladyshev, Supramolecular thermodynamics is a key to understanding phenomenon of life. What is Life from a Physical Chemist’s Viewpoint; Second Ed.; Regular and Chaotic Dynamics: Moscow — Izhevsk, 2003, 144 p. (In Russian).
18. Yu.S. Lipatov, Phase-Separated Interpenetrating Polymer Networks; USChTU (ISBN 966-801
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