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Some notions and terms used in the theory*

HomepageINSTITUTE of Physico-Chemical Problems of EvolutionBiological Evolution and AgingBook Review: G.P. Gladyshev, Thermodynamic Theory of the Evolution of Life FormsSome notions and terms used in the theory*

Complex thermodynamic system - a thermodynamic system where some work aside from extension work is performed (V.Sychev, see reference to Chapter I).

Current quasi-equilibrium - instant equilibrium achieved by a system as a result of fast relaxation. CQE always exists in a quasi-equilibrium, quasi-static process. One can understand CQE as a stationary (time-independent) or quasi-stationary nonequilibrium state of an open system, stable with respect to small perturbations.

Dynamic self-organisation - (or simply self-organisation, in the terminology of I.Prigogine) - a process consisting in the arising, reproduction, or improvement of the organisation of a dynamic system that is far from equilibrium.

Evolution potentials, - specific thermodynamic potentials that determine the changes in thermodynamic potentials (functions) resulting from the variations of the number of particles of certain nature (components of the i-th partial evolutions) of the type k. The EP are analogues of the chemical potential and are used in hierarchic thermodynamics for the description of systems with variable number of particles. The EP can be used in macrothermodynamics for describing the behaviour and evolution of open complex hierarchic non-stationary systems. For example, is the potential of the k-th component, i-th constituent part of the process (partial evolution) taking place in the system j. This notation, used in hierarchic thermodynamics, allows to present the chemical potential of the k-th chemical component in the j-th ideal system as .

Gibbs function (G), or the fundamental Gibbs function, the Gibbs potential, the Gibbs free energy, free energy at constant pressure, free enthalpy, isobaric potential, isobaric-isothermic potential, thermodynamic potential. The GF of a physical-chemical system can be divided into the chemical (molecular) component (ch) characterising the chemical structure of matter, and the supramolecular (im) component characterising the supramolecular structure of matter: . (These structures are formed by chemical and supramolecular bonds, respectively.) Correspondingly, the GF of the formation of condensed matter is represented in the form .

This distinguishing is, in principle, similar to dividing the observed variable D Gobs into the ideal component, D Gideal, and the excess component D GE, which is the Gibbs function of mixing: . The value of D Gideal, for solutions is calculated using the formulas for ideal systems obeying the Raoult`s law for any composition of mixture.

In physical chemistry, one often uses the following values: the Gibbs function of the formation of a compound from the elements and the standard Gibbs function of the formation of a compound from the elements. In hierarchic thermodynamics, if necessary, these values can be denoted as and . According to this notation, the Gibbs function of the formation of the superstructure from chemical compounds, or from a separate compound, can be expressed as , and the standard function as .

Hierarchic thermodynamic system - thermodynamic system consisting of hierarchic subsystems that are related to each other by structure and may be other subordination and by the transitions from lower levels to higher ones. These subsystems should be also separated in space and (or) with respect to the time needed for the relaxation to equilibrium.

Hierarchic thermodynamics (macrothermodynamics, or structure thermodynamics) studies complex heterogeneous chemical and biological systems, first of all, open systems that exchange matter and energy with the environment. According to the approach of HT, such a system should be represented as a set of subordinate subsystems related hierarchically by their positions in space (structural, or spatial hierarchy) and (or) in time (time hierarchy).

The central notion of HT is the notion of partial evolution (the i-th process), i.e., aggregation of the ki-th components of the system participating in the process i on the level j. For example, the negligible non-equilibrium self-assembly process taking place under the melting point of matter can be considered as aggregation of molecules and macromolecules resulting in the formation of supramolecular structures.

Kinetically quasi-closed system - a thermodynamic system open at relatively large times, through which a flow of substance passes and in which, due to thermodynamic factors, comparatively stable substances (for instance, supramolecular structures) are accumulated. This substance accumulation is considered as partial quasi-closeness of the system with respect to some components of the out-coming flow of matter. The system is non-stationary at its times of existence. Kineticaly quasi-closeness of the corresponding subsystems in biological objects is ensured by the hierarchic sequence of thermostats. The existence of this sequence is caused by unidirected series of life (relaxation) - times for structures of different hierarchies.

Life-span (life-time) - the average existence time for a particle or a system (t or ). For non-stable radioactive isotopes or chemical compounds dissociating via first-order reactions, the life-span is defined as , k - being the rate constant, - the half of the life-time. The LS of monomer molecules fed into a polymerization system is determined as the average time spent by a molecule in unbonded (monomer) state. Analogously, one defines the LS of free radicals generated, for instance, by light. The LS of living objects is defined as the life duration of a biosystem, some biostructure (for instance, an organelle, a cell, or an organism), which is defined by the moments of birth and death.

Macrothermodynamics (or hierarchic thermodynamics) studies all sorts of heterogeneous systems (simple and complex) using the methods of thermostatics and non-equilibrium thermodynamics. For example, M of open hierarchic non-stationary systems describes the thermodynamic behaviour of natural systems, for instance, biological ones. The part macro in the term macrothermodynamics is used to stress that this branch of science studies heterogeneous (polyhierarchic) macroobjects. At the same time, thermodynamics of any systems or processes describes the behaviour of systems only on the macroscopic level. From this viewpoint, the part macro in the term macrothermodynamics does not possess any special physical sense.

Ontogenesis - individual development of a living thing, all sequence of its transformations from birth to the end of life.

Partial equilibrium - equilibrium of a physical system with respect to a single or several parameters xi. A system in PR with respect to the parameter xi, can stay non-equilibrium with respect to other parameters xk. For instance, real quasi-equilibrium in hierarchic thermodynamics is a PE established after some i-th partial evolution is accomplished in the given system.

Partial evolution (in hierarchic thermodynamics) - the process of self-assembly (thermodynamic self-organisation) of structures relating to the i-th hierarchy resulting in the formation of structures of a higher hierarchy - (j+1). For instance, the self-assembly of molecules leading to the formation of supramolecular structures can be considered as partial molecular evolution.

Philogenesis - historical development of the world of living organisms both as a whole and in separate taxonomic groups: kingdoms, types, classes, ordos, families, genuses, species.

Population - a group of organisms belonging to a single species, possessing a common genetic fund occupying a definite territory, and, as a rule, more or less isolated from other similar groups.

From the zoological viewpoint, Homo sapiens is a species widely (though inhomogeneously) spread over Earth including numerous populations.

The principle of the stability of a chemical substance is a set of qualititaive regularities according to which the relatively low chemical (ch) thermodynamic stability of a compound in a state of ideal gas or solution () causes relatively high supra-molecular (intermolecular, im) thermodynamic stability of condensed phases formed by that compound (). Conversely, the higher the chemical thermodynamic stability of a substance, the lower its supra-molecular thermodynaic stability in a condensed state. This regularity can be expressed through values of DHcomb , DHform and other functions.

The principle was applied by the author to various hierarchies as part of the theory of the evolution of life. It is in agreement with the principle of structural stabilization.

The principle of the stability of a chemical substance can be applied with a number of qualifications to multi-component systems ( Figures 4 and 7) and reflects the tendency of atoms of different elements to condense around other atoms through chemical and non-chemical (intermolecular, im) ties. The above regularities can be identified for isoatomic substances, several homologous series, lyophilic, lyophobic and biophilic chemical compounds by building the folowing dependencies:


where - coeffcients and the subscript j relates to the substance.

The available data demonstrate that the above relationships cover most simple substances soluble in water.

Precise mathematical formulation of the principle may be impeded, because the measurement of the absolute values of thermodynaic functions is not possible.

Principle of structure stabilisation - the principle stating that in hierarchic systems each higher-level partial evolution or, in other words, higher i-th partial process, which is a component of the general evolution - the process of hierarchic structure formation - stabilises, due to the aggregation, the products of the lower partial evolution, or (i-1)-th partial process. For instance, in a non-stationary open system where various chemical reactions and other processes take place, structure stabilization chooses supramolecular structures that are most stable thermodynamically.

Thermodynamic equilibrium - the state of a thermodynamic system with parameters constant in time. Any system isolated from the environment would spontaneously tend to the TE. As soon as the system reaches TE, all irreversible changes are stopped in it. There exist several conditions of TE relating to the establishment of mechanical, thermal, chemical, social and other types of equilibria in a system. Mechanical equilibrium implies that any macroscopic movements of the parts of the system are prohibited, though the system can move or rotate as a whole. The thermal and chemical equilibria in a system are determined by the condition that temperature and chemical potentials are constant in the volume of the system (or its local microvolumes that can be considered as isolated). Hierarchic thermodynamics also considers other types of equilibrium, which are characterised by constant population, sociological, or other potentials. Like chemical potential, these potentials are defined for the components of the corresponding hierarchies of structures and consideration levels. The conditions for the TE to be stable are obtained from the second law of thermodynamics. It states that the thermodynamic potential of a system is minimal at the TE, while the entropy in this case is maximal (for the corresponding independent variables, i.e., characteristic variables).

Quasi-closed system - a thermodynamic system, open at comparatively large times, which can be considered, to a certain approximation, as closed, due to the fast relaxation to local equilibria (such as supramolecular equilibrium) and (or) due to the partial accumulation of matter coming into the system. In accordance with this general definition, it is worth distinguishing between thermodynamical and kinetical quasi-closeness of a system.

Quasi-static process, or equilibrium process, - an infinitely slow transition of a thermodynamic system from one equilibrium state into another, such that at every time moment the state of the system is infinitely close to the equilibrium state. During a QSP, the system reaches equilibrium much faster (almost instantaneously) than its physical parameters vary. A QSP is not necessarily a reversible process.

Quasi-stationary state in physics - the same as metastable state. A QSS in chemistry and biology is the state of a system involved into a reaction; this state, to a certain approximation, is characterised by constant concentrations of the intermediate products. The concept of QSS can be valid for the description of systems in certain time scales but invalid in other time scales. For instance, a cell, which is a biological system, is not a stationary system at its life-time t. However, at smaller times < < t its behaviour can be considered as stationary; more precisely, quasi-stationary. At the moment of death the cell passes to the state of partial equilibrium (real quasi-equilibrium).

Real quasi-equilibrium - in hierarchic biological thermodynamics (macrothermodynamics), the state of an open system (considered at the given hierarchic level) that is achieved at the moment of death due to the accomplishment of the substance exchange with the environment in the given time scale.

Relaxation - the process leading to the establishment of thermodynamic equilibrium in macroscopic thermodynamic systems. It should be taken into account that the equilibrium state can be determined by a large number of parameters, and the processes of achieving equilibria with respect to different parameters can go in different ways and at different rates. R is quantitatively characterised by the relaxation time.

Simple thermodynamic system - a thermodynamic system where no work or only extension work is performed (V.Sychev, see reference to Chapter I).

Society - any group of organisms belonging to different species coexisting at some territory and interacting through trophic and spatial relations.

Sometimes one specifies S. of plants (phytocenos) and S. of animals (zoocenos). A S. is a system of definite hierarchic level of living matter organisation. Elements of S. are populations of different species. The S. itself is an element of an ecosystem (or biogeocenos).

With certain constraints, one can also use the term society of people as a species including numerous populations.

Stationary state in physics - a state of a physical system where parameters essential for its description do not vary in time. For instance, if the velocity of a flow of fluid is constant at every point, then the state of the flow is stationary. In chemistry, the state of a chemical system involved into a reaction is called SS if the intermediate products of the reaction have constant concentration. In a system with flow (a reactor), concentrations of the components are constant for the SS. In the limiting case, when the flows of matter in an open system tend to zero, the system reaches equilibrium state.

Supramolecular composition of a system - composition of a system consisting of supramolecular components of different nature. For instance, the supramolecular components of a biological membrane, which is a heterogeneous system, are supramolecular formations (aggregates) of proteins, polysugars, lipids, etc.

Synergetics - a frontier branch of science revealing general tendencies in the processes of formation, stability, and destruction of ordered temporal and spatial structures in complex systems of various nature, which are far from equilibrium. The models of synergetics are models of non-equilibrium systems in the presence of fluctuations.

Thermodynamic self-organisation (self-assembly) - spontaneous ordered joining of the structures of i-th hierarchy into structures of (i+1)-th hierarchy. The process of self-assembly (or partial evolution) is a weakly non-equilibrium process similar to phase transition. For instance, formation of supramolecular structures from molecules in a cell can be considered as a phase transition from over-cooled state. Thermodynamic self-organisation is observed in systems close to equilibrium.

TS on the physical-chemical level leads to the association of molecules, macromolecules, or their aggregates. At this process, intermolecular interactions induce changes in the internal structure of molecules, which lead to the appearance of new conformations.

Thermodynamically quasi-closed system - a thermodynamic system open at relatively large times, which can be considered as closed at small times (due to the negligibly small rate of the matter exchange with the environment). For instance, macromolecules in the biotissues of living organisms under physiological conditions form conformations corresponding to the minimum of the Gibbs function; this indicates that the system macromolecule - environment is closed.

Thermostat in the thermodynamics of complex systems - a part of the total system that can be considered as surrounding or environment. The T. imposes certain conditions on the system under study, which is a subsystem of the total system. These conditions can be constant temperature, pressure, chemical potentials or any other potentials (for instance, sociological ones), etc. To avoid the confusion between the definition of T. as a thermal reservoir and the definition given above, it is worth indicating what sense of the term is meant (see R.Kubo, reference to Chapter I).

Time-scale of a process (for instance, rolling up of molecules and formation of globular structures, ontogenesis, philogenesis, etc.) - time interval that is approximately equal to the duration of the process (phenomenon) under study. For instance, the ageing (ontogenesis) of human can be studied in the time scale of about 100 years.

Unidirected series of relaxation times (life-times, or existence times) in hierarchic thermodynamics - a sequence of relaxation times or life-times for structures of different hierarchic levels ordered into a series such that its neighbouring terms are connected by unidirected strong inequalities. USRT reflects one of the fundamental natural laws.

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