Open Systems

thermodynamic systems that exchange mass, as well as energy and momentum, with the environment. The most important type of open systems are chemical systems in which reactions take place continuously, reactants enter from without, and reaction products are removed. Biological systems, or living organisms, may also be considered open chemical systems. Such an approach to living organisms makes it possible to study the processes of the organisms’ development and vital activity on the basis of the laws of the thermodynamics of nonequilibrium processes, physical kinetics, and chemical kinetics.

The properties of open systems are simplest near the state of thermodynamic equilibrium. If the deviation of an open system from thermodynamic equilibrium is small and the system’s state changes slowly, then the nonequilibrium state may be characterized by the same parameters as the equilibrium state, including temperature and the chemical potentials of the system’s components (but with values dependent on the coordinates and time, rather than values that are constant for the entire system). The degree of disorder of such open systems, like the degree of disorder of systems in the equilibrium state, is characterized by the entropy. By virtue of the additivity of entropy, the entropy of open systems in the nonequilibrium (locally equilibrium) state is defined as the sum of the entropies of individual small elements of the systems that are in local equilibrium.

Deviations of the thermodynamic parameters from their equilibrium values (thermodynamic forces) induce fluxes of energy and mass in a system. The transfer processes that take place lead to an increase in the system’s entropy. The entropy increment of the system per unit time is called the entropy production.

According to the second law of thermodynamics, in a closed isolated system the entropy increases, tending toward its maximum equilibrium value, whereas the entropy production tends toward zero. In contrast to a closed system, steady states with constant entropy production are possible in open systems; in this case the entropy must be removed from the system. Such a steady state is characterized by constant rates of chemical reactions and of the transfer of reactants. In such “flowing equilibrium,” entropy production in an open system is minimal (the Prigogine theorem). The steady nonequilibrium state plays the same role in the thermodynamics of open systems as does thermodynamic equilibrium for isolated systems in the thermodynamics of equilibrium processes. The entropy of an open system in this state is held constant, since its production is balanced by removal from the system, but this steady-state value of entropy does not correspond to maximum entropy, as in an isolated system.

The most interesting properties of open systems are displayed in nonlinear processes. In such processes, thermodynamically stable nonequilibrium states—in particular, steady states—remote from the state of thermodynamic equilibrium and characterized by some spatial or temporal order (structure), which is called dissipation structure because its existence requires continuous exchange of mass and energy with the environment, can be achieved in open systems. Nonlinear processes in open systems and the possibility of forming structures are studied using the equations of chemical kinetics: the balance of the rates of chemical reactions in a system with the rates of supply of reactants and the rates of removal of reaction products. The accumulation of active reaction products or heat in open systems may lead to a self-oscillating (self-sustaining) reaction mode. For this to occur, positive feedback must be present in the system in the form of acceleration of the reaction either by the reaction’s product (chemical autocatalysis) or by the heat released during the reaction. In the same way as stable, self-regulating sustained oscillations, or self-oscillations, arise in an oscillatory circuit with positive feedback, sustained self-regulating chemical reactions arise in open chemical systems with positive feedback. Autocatalytic reactions can lead to instability of chemical processes in a homogeneous medium and to the appearance of steady states in open systems with an ordered spatial nonuniform distribution of concentrations (dissipation structures with order at the macroscopic level). The nature of the structures is determined by the specific type of chemical reaction. Concentration waves of a complex nonlinear nature are also possible in open systems.

The theory of open systems is important for understanding the physicochemical processes underlying life, since a living organism is a stable self-regulating open system that has a high level of organization on both the molecular and macroscopic levels. The treatment of living systems as open systems in which nonlinear chemical reactions take place opens up new possibilities for study of the processes of molecular self-organization at the early stages of the evolution of life.

The theory of open systems is a particular case of the general theory of systems, which include data-processing systems, transportation junctions, power-supply systems, and others that are treated in cybernetics. Such systems, although not thermodynamic, can be described by a system of balance equations that in the general case are nonlinear and analogous to those considered for physicochemical and biological open systems. Common problems of regulation and optimum functioning exist for all systems.