Thermodynamic evolution criteria

In order to extract the maximal energy out of the available foodstuff oxidative phosphorylation should operate at the state of optimal efficiency in vivo. Since a zero as well as an infinite load conductance both lead to a zero efficiency state, obviously there must be a finite value of the load conductance permitting the operation of the energy converter at optimal efficiency. For linear thermodynamic systems like the one given in equations (1) and (2) the theorem of minimal entropy production at steady state constitutes a general evolution criterion as well as a stability criterion.3 Therefore, the value of the load conductance permitting optimal efficiency of oxidative phosphorylation can be calculated by minimizing the entropy production of the system (oxidative phosphorylation with an attached load)... 

Let us say that the system has only one independent variable Y for example, the concentration (thermodynamic rush) of some intermediate. In this case, the evolution criterion d P < 0 can be expressed in the form of total differential (3.4)... 

The Glansdorff-Prigogine general evolution criterion, in case of time independent boundary conditions, which are valid during the evolution of the thermodynamic steady state, can be formulated as... 

According to the Glansdorff-Prigogine general evolutions criterion (192), from the above equation we get the necessary conditions of the minimum of the entropy production at the thermodynamics steady state... 

The minimum entropy production theorem dictates that, for a system near equilibrium to achieve a steady state, the entropy production must attain the least possible value compatible with the boundary conditions. Near equilibrium, if the steady state is perturbed by a small fluctuation (8), the stability of the steady state is assured if the time derivative of entropy production (P) is less than or equal to zero. This may be expressed mathematically as dPIdt 0. When this condition pertains, the system will develop a mechanism to damp the fluctuation and return to the initial state. The minimum entropy production theorem, however, may be viewed as providing an evolution criterion since it implies that a physical system open to fluxes will evolve until it reaches a steady state which is characterized by a minimal rate of dissipation of energy. Because a system on the thermodynamic branch is governed by the Onsager reciprocity relations and the theorem of minimum entropy production, it cannot evolve. Yet as a system is driven further away from equilibrium, an instability of the thermodynamic branch can occur and new structures can arise through the formation of dissipative structures which requires the constant dissipation of energy. 

To coordinate components, the generalized flows and the thermodynamic forces can be used to define the trajectories of the evolution of nonequilibriun systems in time. A trajectory specifies the curve represented by the flow and force components as a function of time in the flow-force space. A useful trajectory can be found and analyzed by a variation principle. In thermodynamics, the variation principles lead to the least energy dissipation and minimum entropy generation at steady states. According to the most general evolutionary criterion, open chemical reaction systems are dissipative, and evolve toward an asymptotic state in time. 

The deduction of a criterion for the evolution of an open system to its stationary state resembles the classical thermodynamic problem of predict ing the direction of spontaneous irreversible evolution in an isolated system According to the Second Law of thermodynamics, in the latter case the changes go only toward the increase in entropy, the entropy being maximal at the final equilibrium state. 

The Prigogine Criterion (Theorem) of the Evolution for Systems that Are Close to their Thermodynamic Equilibrium... 

Therefore, the principle of the minimal rate of entropy production appears to be the quantitative criterion (i.e., the necessary and sufficient condition) to determine the direction of spontaneous evolutions in any open systems near their thermodynamic equifibrium. In other words, this is the quanti tative criterion of the evolution of a system toward its stationary state. In an isothermal system, the principle of the minimum of the entropy production rate is fuUy identical to the principle of the minimum of the energy dissipation rate. The last principle was formulated by L. Onsager... 

The Onsager reciprocal relations are not satisfied in open strongly non equilibrium systems. As a result, the assumption on minimization of the entropy production rate is not substantiated. Therefore, the universal criterion of the system that is evolution far from equilibrium should be a generalization of the principle of the minimized entropy production rate in specific terms of nonlinear thermodynamics. 

Inequalities (3.2) and (3.3) are generalizations of the principle of the minimal entropy production rate in the course of spontaneous evolution of its system to the stationary state. They are independent of any assump tions on the nature of interrelations of fluxes and forces under the condi tions of the local equilibrium. Expression (3.2), due to its very general nature, is referred to as the Qlansdorf-Prigogine universal criterion of evolution. The criterion implies that in any nonequilibrium system with the fixed boundary conditions, the spontaneous processes lead to a decrease in the rate of changes of the entropy production rate induced by spontaneous variations in thermodynamic forces due to processes inside the system (i.e., due to the changes in internal variables). The equals sign in expres sion (3.2) refers to the stationary state. 

Obviously, the Glansdorf Prigogine universal criterion of evolution (3.2) is an indirect consequence of the Second Law of thermodynamics for... 

The matrix eigenvalues are analyzed for the stationary state in respect to the concentrations of aU independent intermediates. In the thermody namic representation of kinetic equations, independent variables that describe the system evolution in time are not the concentrations but ther modynamic rushes A of the intermediates. Hence, the analysis of the sta bihty criterion in terms of thermodynamic variables needs an inspection of eigenvalues of matrix M p = However, the specific form of the... 

From the second law of thermodynamics, we know that all natural processes tend to approach equilibrium spontaneously, energy being required to drive the system away from equilibrium. The second law provides us with a criterion of spontaneity, i.e., whether a given process (e.g., biochemical or biophysical reactions) is feasible under a specified set of conditions. It points the direction for the evolution of physicochemical processes since it capsulizes the observation that, in all processes, some of the energy becomes unavailable to perform work, owing to the increased random motion of some of the component molecules of the system. In other words, the second law distinguishes between irreversible processes, which by their very nature are unidirectional, and reversible processes, which are bidirectional. 

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