Law of temporal hierarchies

In hierarchical thermodynamics, law of temporal hierarchies states that any living system of any temporal hierarchical level in a normal state has a "thermostat", which is a surrounding medium that is characterized by slightly changing average values of thermodynamic parameter. In simple terms, the law of temporal hierarchies is a means of identifying or discerning a systems-within-systems point of view in the classical thermodynamic anaysis of living system both internally and socially. This law was formulate by Russian physical chemist Georgi Gladyshev beginning in 1978. As a general rule, according to Gladyshev, the higher the hierarchy, the smaller the energy of interaction between the particles. [1]

The justification of this statement is connected with the phenomenon of metabolism and the exchange of matter and energy between adjoined hierarchies. Lower level hierarchical molecular structures are often reproduced in a medium of higher level hierarchical molecular structures during the lifetime of the latter. Thus, we have:

ti << ti+1

As a rule, modern thermodynamics studies simple or complex systems with similar processes taking place in a single fixed time scale. Usually, the processes are localized in one or several hierarchies. However, the processes in real systems usually imply complicated transformations involving structures of various hierarchies and relating to different time scales. In this situation we use the full differential equations and characteristic functions defined for macrothermodynamics - thermodynamics of complex hierarchic natural systems at constant temperature and pressure.

In such hierarchic systems, not only do chemical reactions take place but also transformations between the structure elements of other j-th hierarchic levels (i-th partial evolution). Moreover, let the reagents of each i- th evolution condense into the particles of the i-th evolution phase - a structure of higher level of substance organization. In their turn, the latter are reagents of the next, (i+1) -th, partial evolution. (The order of the partial evolution, i and of the structure hierarchy, j corresponds to the hierarchy order of the reagents.) Transformation of similar reagents of some hierarchic level (j) into similar reagents of the next hierarchic levels (j+1, j+2,...) can be represented as using a system of bi-directional two-way transition reactions arrows. This law is based on the observation that different structures delineate into different classifications of separate yet connected reacting systems distinguished by life-span (t):

... << tmol << tcel << torg << tpop << ...
Where ti is the average lifetime of the molecular structures of the lower temporal hierarchical level and ti+1 is the average lifetime of molecular structures of higher temporal hierarchical level. This law justifies the use quasi-closed equilibrium thermodynamic models to investigate open living systems. These distinctions are important in justifying a Gibbsian thermodynamic analysis of human life. In making this distinction, we now theoretically define, subgroup, or compartmentalize different interactive reactive living systems into separate yet connected quasi-equilibrium hierarchic thermodynamic systems, which can be defined as: thermodynamic systems consisting of hierarchic subsystems that are related to each other by structure and may be other subordination and by the transitions from lower level to higher ones. These subsystems should be also separated in space and or with respect to the time needed for the relaxation to equilibrium.

Using the law of temporal hierarchies, Gladyshev for the first time has strictly proved a possibility to apply the methods of the classical thermodynamics (the methods of the quasi-equilibrium thermodynamics) for studying the individual mono-hierarchical quasi-closed systems in living polyhierarchical open systems. It has allowed to show, that the thermodynamics is convenient for research the interactions between similar mono-hierarchical particles in near-equilibrium systems. To apply thermodynamics to the poly-hierarchical system, as a rule, has no physical sense, as this system is composed of particles of different nature. It is not possible to use linear equations for the research of this system. From this point of view it is possible to analyze a correctness of use of thermodynamics by different authors. For example, R.Clausius and J.W.Gibbs stated: “Die Energie der Welt ist constant. Die Entropie der Welt strebt einem Maximum zu.” Here it is necessary to keep in mind, that 'Der Welt' – the Universe of Clausius and Gibbs – is a model of isolated ideal simple thermodynamic system, where no work or where only extension work is performed. Many authors often forgot about this important circumstance. As result of it in science there are many misunderstanding connected with concept “entropy”.

1. Discussions between Georgi Gladyshev and Libb Thims in Chicago on Dec. 17, 2007.

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