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