Minimal entropy production

Figure 5.21 Bifurcation far from equilibrium, (a) Primary bifurcation is the distance from equilibrium, at which the thermodynamic branching of minimal entropy production becomes unstable. The bifurcation point or critical point corresponds to the concentration (b) Complete diagram of bifurcations. As the non-linear reaction moves away from equilibrium, the number of possible states increases enormously. (Adapted, with permission, from Coveney and Highfield, 1990).

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)... 

The affinity of the net reaction is maintained at a constant value by the flows of H2 and Br2. One of the reactions is unconstrained. Show that the stationary state leads to minimal entropy production. 

Example 4.8 Chemical reactions and reacting flows The extension of the theory of linear nonequilibrium thermodynamics to nonlinear systems can describe systems far from equilibrium, such as open chemical reactions. Some chemical reactions may include multiple stationary states, periodic and nonperiodic oscillations, chemical waves, and spatial patterns. The determination of entropy of stationary states in a continuously stirred tank reactor may provide insight into the thermodynamics of open nonlinear systems and the optimum operating conditions of multiphase combustion. These conditions may be achieved by minimizing entropy production and the lost available work, which may lead to the maximum net energy output per unit mass of the flow at the reactor exit. 

Consider a simple mixer for extraction. In minimal entropy production, size I. time t. and duty J are specified and the average driving force is also fixed. We can also define the flow rate Q and the input concentration of the solute, and at steady state, output concentration is determined. The only unknown variables are the solvent flow rate and composition, and one of them is a decision variable specifying the flow rate will determine the solvent composition. Cocurrent and countercurrent flow configurations of the extractor can now be compared with the... 

Configurations that minimize s2(X) and s2 q) also minimize entropy production and lead to thermodynamically optimum configurations. Such thermodynamic analysis will contribute to the study of feasibility and economic analysis after relating the level of entropy production to engineering economics. 

From the perspective of the fluctuation-dissipation approach, Dewey (1996) proposed that the time evolution of a protein depends on the shared information entropy. S between sequence and structure, which can be described with a nonequilibrium thermodynamics theory of sequence-structure evolution. The sequence complexity follows the minimal entropy production resulting from a steady nonequilibrium state... 

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. 

The experimental investigations prove the validity of the reciprocal relations for several types of irreversible processes moreover, as we show below the linear and generalized reciprocal relations are clear phenomenological consequence of the principle of minimal entropy production. Consequently, the generalized reciprocal relations are reasonably well-established thermodynamic law, however of course it has no such general validity as the basic laws of thermodynamics, (e.g. the energy conservation or the direction of the spontaneous thermodynamic processes). 

Consider the earlier fixed (67) boundary conditions for these partial differential equations and start again with the OM-function of the generalized Onsager constitutive theory to explain the principle of minimal entropy production... 

The minimal entropy production has general consequences on the geometry of the vascular network. The most impwrtant one that the supply-network must not have loops, otherwise we could neglect this hypothetic loop without changing the supply with blood in any of the junction points. Also, we could decrease the entropy production without the missing supply of the junctions. The network, which has no loops called tree. So the minimal entropy production guarantees the tree-character of the vascular geometry. 

The other important characteristic of bifurcation pattern is the bifurcation angle (see Fig. l.a.), which also satisfies the minimal entropy production principle. To prove this consider the junction geometry determined by the A, B, and C points in Fig. l.b. Its entropy... 

The above parts show the minimum principle for vector processes in the frame of the generalized Onsager constitutive theory by the directions of Onsager s last dissip>ation of energy principle. We had seen above that in case of source-free balances, this principle is equivalent with the principle of minimal entropy production. The equivalence of the two theorems in the frame of the linear constitutive theory was proven by Gyarmati [2] first. Furthermore, we showed that in case when the principle of minimal entropy production is used for the determination of the possible forms of constitutive equations, the results are similar to the linear theory in the frame of the Onsager s constitutive theory, where the dissipation potentials are homogeneous Euler s functions. 

Calculate the potential-drop on a given resistivity in an arbitrary DC circuit. Prove that this task could be solved by the minimization of the sum of dissipation potentials or by the principle of minimal entropy production, like we did in the serial connection of the Figure 5., when the circuit regarding the contacts of the resistor is replaced with the Thevenin s potential source equivalent circuit p],... 

Lebiedz, D. Computing minimal entropy production trajectories an approach to model reduction in chemical kinetics. J. Chem. Phys. 120, 6890-6897 (2004)... 

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