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Hierarchical thermodynamics

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Hierarchical thermodynamics, also called macrothermodynamics or structural thermodynamics is a modern phenomenological thermodynamic theory that studies complex heterogeneous chemical and biological systems, primarily open systems, exchanging matter and energy with the environment.[1][2][3][4]. Hierarchical thermodynamics is the thermodynamics of systems close to an equilibrium state, when the state functions of evolving systems have real physical meaning. Hierarchical thermodynamics is a quasi-equilibrium dynamic thermodynamics created on the foundation of J.W. Gibbs equilibrium thermodynamics[5] Hierarchical thermodynamics is a branch of classical thermodynamics, which considers evolutionary systems on a long time scale as open for the exchange of matter and energy with the environment. However, on short time scales, in small evolution windows, when it can be assumed that hierarchical subsystems are located in physical thermostats, they (subsystems) are considered as thermodynamically closed (quasi-closed), to which, therefore, we apply classical thermodynamic analysis. Hierarchical thermodynamics is discussed on many sites in the Internet. However, it is very important to keep in mind that some terminology used by certain authors is not welcomed by modern science[6] The foundations of hierarchical thermodynamics were created by G. P. Gladyshev[7] in the late 1970s. Hierarchical thermodynamics is a further development of Gibbs theory and to within a known approximation is applied to systems of all temporal (structural) hierarchies of real world. Especial interest is the application of hierarchical thermodynamics to real living systems which, as before believed, could not be investigated by classical thermodynamics methods. The reason of this was the statement that natural biological systems are open and that these systems are far from an equilibrium state. Recently, however, the law of temporal hierarchies was discovered. This law substantiates the possibility of identifying, or discerning, quasi-closed mono-hierarchical systems or subsystems within open poly-hierarchical biological systems. It was also established that the processes of evolution in living natural systems, as a rule, are quasi-equilibrium processes. Then it was shown that models of living systems are analogues of models of quasi-equilibrium chromatographic columns. Hierarchical thermodynamics has found applications in areas of anti-aging science and human chemistry (EoHT). Hierarchical thermodynamics is the basis of the thermodynamic theory of the origin of life, its evolution and the aging of living beings. The theory was created on the solid foundation of expanded thermodynamics of J. W. Gibbs. Theory is the physical foundation of expanded Darwinism.

Theory of the origin of life, its evolution and aging of living beings[edit]

The law of temporal hierarchies and evolution[edit]

The hierarchy of living structures in the real world exists as a result of the action of the general law of nature - the law of temporal hierarchies. This law states that there are unidirectional series of strong inequalities of lifetimes of hierarchical structures: molecules, cells, organisms, populations and so on[8][9]. Each type of organism is characterized by its own individual series. In general, the law can be presented in the form:


Here is the average lifetime of the structure j of the lower hierarchical level, is the average lifetime of the structure (j+1) of the higher hierarchical level. If we consider the main hierarchical levels of a particular type of organism, then we can write:

… (2)

Here t is the average lifetime of “free” molecules of metabolites (m); "free" supramolecular structures (im); organelles; cells (cell); organisms (org); populations (pop); communities (soc). The exchange of hierarchical structures in organisms and higher hierarchies is a consequence of the existence of a series (1): the structures of lower hierarchies, for example, cells, live significantly less than the structures of higher hierarchies, for example, organisms. Of course, that without metabolism, life could not exist. Rows (1) and (2) represent the overlapping sequence of the triads of Nikolai Bogolubov.[10]. This means that the processes within each hierarchy with a certain approximation can be considered independent of the processes occurring in other hierarchies. However, adjacent hierarchies still interact with each other. These interactions can be seen in terms of the “variation and selection” of Darwinism. In other words, the principles of the theory of C. Darwin and A. Wallace can be extended to the chemical, geological, and other components of the overall evolution of matter. The law of temporal hierarchies is the substantiation of hierarchical thermodynamics, the mathematical formalism of which is entirely similar to the mathematical formalism of classical thermodynamics of C. Carathéodory and other classics[11]. One of the important principles of the thermodynamic theory of evolution is the statement that nature seeks maximum stability at all hierarchical levels[12]. The above search for the stability of evolving systems according to the second law is a spontaneous process that takes place against the background of non-spontaneous processes in these systems, processes initiated by the environment. Chemical evolution proceeds at various temperatures, pressures and other physical effects in space, as well as on celestial bodies, where it is accompanied by geological evolution. As a result of numerous chemical transformations, primary “building blocks of life” are formed, which, if there are conditions for the emergence and development of life, participate in the appearance of organisms. Chemical evolution smoothly transfers into biological evolution. One of the important processes of this transition is the formation of constantly updated supramolecular structures, which, as a result of the principle of substance stability, are enriched with energy-intensive molecular structures. Further, the principle of substance stability applies to higher hierarchies, which means the appearance of higher forms of living matter. It is important to clarify the accuracy of the hierarchical thermodynamic theory, which is built on the foundation of the exact Gibbs theory. The accuracy of the hierarchical thermodynamics model is determined by the strong inequalities (1) and (2). The stronger these inequalities, the closer the model approaches the exact Gibbs model. However, for accurate estimates it would be necessary to know the absolute values ​​of the Gibbs free energy of the formation of chemical elements (simple substances). Currently there is no such information. This circumstance forces us to use the rough idea of ​​the thermodynamic uniformity of biogenic elements to explain and predict natural phenomena. The approximation used makes it possible to identify the directional tendency of the development of chemical and biological evolution.

The principle of substance stability[edit]

Hierarchical thermodynamics based on the principle of substance stability is able to explain and predict directional variations in chemical and biological evolution and to verify the assertion that Nature tends to the maximum structural stability at the molecular and supramolecular levels. The principle of substance stability, or the feedback principle, was formulated by Georgi Gladyshev in 1977. Later, considerations concerning physical verification of the principle were presented. The considerations were based on simple concepts[13][14][15]. It was stated that each atom, molecule, an isolated supramolecular structure (or structure of higher hierarchy) has a potentially limited capability of participating in interactions with other atoms, molecules, and supramolecular or other structures. It was assumed that if particle i of hierarchy j (or subhierarchy j) spent much energy for binding to another particle of the same hierarchy j, there remains rather little energy in this particle i for binding to other particles of its hierarchy or particles of higher hierarchies (j+1). For instance, if a molecule (formed by strong chemical bonds) is relatively thermodynamically stable, it is unable to form rather stable structures that arise during formation of supramolecular structures (aggregates). Isolated supramolecular structures of the lower hierarchy j (consisting of a relatively small number of molecules) can participate in formation of supramolecular j+1 structures (consisting of a large number of particles) in accordance with their limited energy capabilities. It is established that the principle of substance stability acts at all hierarchical levels and sublevels of systems in all hierarchies of living matter. The principle of substance stability plays a decisive role at particular stages of chemical evolution. It is the driving force of the origin of life, biological evolution, phylogenesis, and ontogenesis. The principle can be formulated as follows: «During the formation or self-assembly of the most thermodynamically stable structures at the highest hierarchical level (j), e.g., the supramolecular level, Nature, in accordance with the second law, spontaneously uses predominantly the least thermodynamically stable structures available from a given local part of the biological system, belonging to a lower level, i.e., the molecular level (j-1), and incorporates these unstable structures into the next higher level, i.e. the supramolecular level (j)». The principle of substance stability made it possible to identify the tendency of evolutionary development and the transformation of structures at all hierarchical levels: atomic, molecular, supramolecular, cellular, organism, social, and other levels.

Gibbs free energy change during evolutionary transformations[edit]

All spontaneous (spontaneous) and non-spontaneous (non-spontaneous) changes in evolving natural systems are accompanied by changes in the Gibbs specific free energy (Gibbs function) of the formation of these systems. Often in evolution, spontaneous transformations in natural systems occur against the background of minor non-spontaneous changes in these systems, that is, processes initiated by the environment. In such cases, these natural systems can be considered quasi-closed and their evolution can be studied by measuring the Gibbs specific free energy of formation of these systems. The indicated change according to the second law of thermodynamics will be less than zero. The magnitude of this change with good approximation characterizes evolutionary processes close to equilibrium in all the hierarchies of the living world. These considerations characterize evolutionary changes in the systems under consideration. However, in the event of revolutionary changes in the environment (the fall of meteorites, volcanic eruptions, earthquakes and other similar phenomena), the direction of evolutionary changes becomes unpredictable. In such cases, it is possible to break the evolutionary spiral, which can lead to the cessation of life in the areas of these revolutionary influences. Figure 1 shows the spiral of evolution, which is actually a physical and artistic symbol of its thermodynamic directionality.

Credit: Graham, Joseph, Newman, William, and Stacy, John, 2008, The geologic time spiral—A path to the past (ver. 1.1): U.S. Geological Survey General

Fig.1- Spiral of evolution, the symbol of its thermodynamic directionality

In the general case of complex thermodynamic systems (systems in which not only expansion works take place), the Gibbs free energy change can be estimated using one of the forms of the extended generalized Gibbs equation - the generalized equation of the first and second principles of thermodynamics[16][17]:


Where G is the Gibbs free energy; T is the temperature; S is the entropy; V is the volume; p is the pressure; X is any generalized force except pressure; x is any generalized coordinate except volume; µ is the chemical (evolutionary) potential; m is the mass of the k-substance; the work performed by the system is negative. The subscript i pertains to the specific evolution, and k to the component i evolution. The superscript * means that behavior of a quasi-equilibrium complex system is considered. The above equation is a generalized equation since in principle all interactions (inside and outside) of all structures of every hierarchical level are taken into consideration independently of the scale of these interactions. It is logical to consider this equation as one with considerably divided parameters, symbolic or speculative, that can be efficiently used only in relation to everyone or adjacent hierarchies of structures. In this case, the Gibbs equation is considerably simplified in connection with negligibly small values of the majority of its isolated or individual members. Symbolism or speculation consists in the fact that it is difficult to take into consideration simultaneously all multi-scale effects determining the behavior of complex heterogeneous poly-hierarchical system at once. This statement is connected to the principle of mathematics, which allows us to combine like with like only and prefers the simplicity and unity in the description of the physical picture of the real world. Although, it should note that the above equation is characterized by a unity that is associated with a general thermodynamic approach to study the behavior of all individual mono hierarchical systems that form polyhierarchical systems. Importantly, the simplified relations obtained from equation (3) are used in the study of tropisms and in many physiological and other studies ]. The law of temporal hierarchies first substantiated the correctness of these approaches based on thermodynamics. It should also be noted that the present equation must contain terms that take into account the interaction between biological objects (e.g. cells, organisms and other structures) arising from actions, physical fields and radiation, the origin of which is associated with chemical and physiochemical processes in living systems. Many that are often not strictly identified as "weak" interactions in the living world can be attributed to tropisms, which detail the mechanisms of these interactions, are not clear. The complexity of studying these phenomena, as a rule, is the lack of highly sensitive physical devices that measure these interactions. However, biological sensors can detect these mutual effects of biological objects. Thus it can be argued that the transfer of "structure information" between biological molecules and supramolecular structures by organisms do not necessarily require direct close contact of the said structures (e.g. information transfer that occurs at the contact of nucleotides during the formation of DNA or during the formation of acetic acid dimers).

Thermodynamics of aging[edit]

The thermodynamic theory of aging is part of a more general theory of the origin of life, its evolution and the aging of living beings. From the point of view of hierarchical thermodynamics, ontogenesis, as a rule, practically repeats phylogenesis. This statement was justified after it was proved that the change in chemical and supramolecular composition has a thermodynamic nature. It is possible to investigate the development (ontogenesis) and evolution (phylogenies) of living beings by studying the changes of the value of specific (per unit of volume or mass) Gibbs free energy of the formation of the given higher hierarchical structure out of lower-level structures. Thus, it was established that in ontogenesis (or phylogenies), the specific Gibbs function of the formation of supramolecular structures of an organism’s tissues () tends to be a minimum:


where V is the volume of the system; m is the mass of the identified micro-volumes; x, y, z are coordinates; symbol «–» means that the value  is specific; and symbol «~» emphasizes the heterogeneous character of the system. The equation (4) implies taking account of all supramolecular interactions in all hierarchical bio-tissue structures (intracellular, intercellular and others). Sometimes the organism of living being is investigated as complex non-steady state chromatograph column, such that upon digestion of food-stuffs, in which some part of sustenance first reacts with hydrochloric acid and enzymes to break-down in the stomach, the nutritive particle molecules will then each migrate to different parts of the organism molecular structure based on their relative thermodynamic stability and their relative chemical affinities for different intra-molecular attachment sites within the body. This model allows the thermodynamic theory of aging to be called the chromatographic theory of aging. For several decades, the predictions of the thermodynamic theory of aging have been confirmed in practice[18]. This is especially true of predictions in the field of nutrition and pharmacy. (Aging, EoHT) However, there is no direct unequivocal evidence of the effect of diets and food additives on a person’s life expectancy[19]. However, from the position of the thermodynamic theory, the effect of food features on the life expectancy of animals and humans was predicted, and appropriate recommendations were made in one of the articles that are devoted to this issue. There one can read the following[20]: “From the perspective of the thermodynamic theory of aging, it is advisable to take into account gerontological G. P. Gladyshev’s value indicators of food products and medicinal preparations, gerontological purity of drinking water... However, in practice, it is convenient to follow the recommendations listed below. To use as much as possible clean drinking water, the consumption of which is not contrary to medical indications. To eat biomass of phylogenetically young (ancient) species of plants and animals — relatively young food (for instance, algae, some species of fish and amphibians) . To eat biomass of ontogenetically young plants and animals—relatively young food (germinated seeds, animals’ germs, maggots, roe, young mammals, juvenile fish, chicks, etc.). Preference should be given to: Seafood, especially products of cold seas and rivers; Biomass of plants and animals growing and living in cold regions: the extreme northern and southern areas of the planet, highlands; Fats and oils with low melting points (algae oil, flax seed oil, cedar wood oil, sunflower oil, corn oil, soybean oil). In case of propensity for diabetes and some other pathology, it is advisable to prefer vegetables instead of fruits. Besides, it is recommended to minimize consumption of carbohydrate-containing products (for instance, bread and floury products, rice, potatoes). It is recommended to use food extracts and medicinal extracts of young medicinal plants growing in cold regions. It is recommended to avoid eating overdone and processed food products with carcinogenic properties. Avoid taking medicines and food supplements with a low gerontological value. The specified recommendations agree with the centuries-old human experience”. All recommendations submitted, if reasonably applied, are confirmed[21]. Thus, very important results (predicted by the thermodynamic theory of aging) were obtained in experiments on animals[22].

Confirmed predictions[edit]

Hierarchical thermodynamics, despite a number of approximations, can explain many known facts and make a number of predictions[23]. Until now any events and facts are not aware in the life sciences, which cannot be understood at least in principle, from the perspective of thermodynamic theory of origin of life, its evolution and aging of living beings. In 1977 it was shown that the variation of chemical and also supramolecular composition of living beings is a result of the action of laws of hierarchical thermodynamics. The theory predicted enrichment of living beings by heavy isotopes and heavy chemical elements during evolution. The thermodynamic theory explained the nature of molecular selection in evolution including the selection of lipids, proteins and nucleic acids from the viewpoint of physical chemistry. It was termed as thermodynamic dietetics. On the basis of calculations presented, some recommendations were made regarding the establishment of anti-aging diets prolonging healthy life of animals and humans. These recommendations are fully consistent with the experience of ancient and modern medicine, and nutritional science. Furthermore, the theory has made a number of completely new, practically important, recommendations in sport medicine, pharmacology and other areas of expertise. It can be argued, that through the principle of substance stability, hierarchical thermodynamics determines the natural selection of elements, molecules and structures of the higher hierarchies during the origin of life and biological evolution. This area of science has accumulated a lot of important information which should be carefully analyzed from the standpoint of thermodynamic selection. Hierarchical thermodynamics allows us to understand social phenomena. From the standpoint of thermodynamics we can understand the ancient principle of "divide and rule". It is also shown that for most times the history of the development of society is predictable. On the basis of thermodynamic theory, hypotheses on the origins of cancer, the nature of some pathology, the common (identical) genetic code in the universe, and about the phenomenon of life as self - defending process can also be formulated. In recent years, attention was drawn to the opportunity to explain the phenomenon of natural selection based on thermodynamic concepts of the dynamical mechanism of this phenomenon. Thermodynamic theory, based on new data banks[24], revealed the directionality of changes in the chemical stability of metabolite molecules and supramolecular structures of organisms under physiological conditions. On the basis of experimental data, it was established that during evolution chemical and biological objects in accordance with thermodynamic theory are enriched with nitrogen and phosphorus. In addition, it was found that it is necessary to review the results regarding the stability of the high-energy phosphates and other metabolites[25]

On the recognition of evolutionary thermodynamic theory[edit]

The first article on thermodynamics of biological evolution was published in Russian and English as a preprint at the Institute of Chemical Physics of the USSR Academy of Sciences in May 1977[26]. In this work, in fact, it was about the development and expansion of theory of J.W. Gibbs and the application of the extended theory to dynamic systems close to equilibrium. In other words, the article dealt with a new branch of thermodynamics — classical thermodynamics of natural systems. This work was sent to the Journal of Theoretical Biology, USA. The article was reviewed 8 times. Editor-in-chief of Journal Dr. James Danielli, F.R.S. informed the author of the article that reviewers had difficulty in estimation of the work, since it can be extremely outstanding. Dr. James Danielli made the sole decision and published an article in the journal[27]. After publication the article was welcomed by many physicists and physicists-chemists. However, very few biologists have shown interest in the new theory for many years. One of the reasons for this was due to the fact that the new theory was in direct conflict with the fashionable theory of systems far from equilibrium of Dr. I. Prigogine. In addition, the awareness of new theory created great difficulties associated with the use of a broad interdisciplinary approach. Moreover, there were very few experimental data witch confirmed the reasonableness of using the models under consideration. Now the attention to the theory has increased significantly due to the interest in the problems of the origin of life, chemical and biological evolution and aging of living beings[28][29]. The emergence of free access logs online also contributed to this.


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  11. Eloshvili S. A. (Tbilisi, Georgia). On the mathematical foundations of hierarchical thermodynamics (in Russian) pdf
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  18. Gladyshev G.P., Thermodynamics of the origin of life, evolution, and aging, Advances in Gerontology; 2015, Vol. 5, Issue 2; pp. 55-58. Original Russian Text © G.P. Gladyshev, 2014, published in Uspekhi Gerontologii, 2014, Vol. 27, No. 2, pp. 225–228.
  19. Ageing.
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  21. Gladyshev, G. (2015) Thermodynamics of Aging and Heredity. Natural Science, 7, 270-286. doi: 10.4236/ns.2015.75031
  22. Sang-Goo Lee, Alaattin Kaya, Andrei S. Avanesov et al., Age-associated molecular changes are deleterious and may modulate life span through diet, Science Advances 17 Feb 2017:Vol. 3, no. 2, e1601833 DOI: 10.1126/sciadv.1601833.
  23. Georgi P. Gladyshev (2015) Natural Selection and Thermodynamics of Biological Evolution. Natural Science, 07, 117-126. doi: 10.4236/ns.2015.73013
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  25. Gladyshev G.P. On the thermodynamics of a high-energy phosphate pool in biochemistry, Norwegian Journal of development of the International Science; ISSN 3453-9875; 2018; Vol. 2; No. 18; pp. 18-21.
  26. Gladyshev G. P. On the Thermodynamics of Biological Evolution, Preprint, Chernogolovka, Institute of Chem. Phys. Academy of Science of USSR, May, 1977, p. 46. Т 05140 27.V 1977.
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  28. Spyros G Tzafestas. Energy, Information, Feedback, Adaptation, and Self-organization: The Fundamental Elements of Life and Society. Springer International Publishing, Jan 29, 2019 - Technology & Engineering - 668 pages.
  29. G.A. Mansoori, N. Enayati and L.B. Agyarko, “Energy: Sources, Utilization, Legislation, Sustainability, Illinois as Model State”, 812 Pages, World SCi. Pub. Co & Imperial College Press, 2016.

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