Biological Membranes - A. N. Ogurtsov 2012

Electrogenesis of Biomembranes
Nonequilibrium Thermodynamics of Biomembranes
Thermodynamics of Systems Far from Equilibrium

The possibility of a spontaneous transition of an isolated system between two states can be determined using classical Thermodynamics by comparing the Entropy values of these states. In an open system, stationary states arise that may lie far from thermodynamic equilibrium.

The possibility of an open system transitioning from a given initial state to a final stationary state, provided both states are near thermodynamic equilibrium, is determined by Prigogine's theorem. However, far from equilibrium, it is no longer possible to draw unambiguous Conclusions about how The rate of entropy production changes as the system approaches a stationary state.

The evolution of such non-equilibrium dynamic systems is determined primarily by The kinetics of interaction among their constituent elements, rather than by the statistical ordering of the initial and final states as described by classical thermodynamics. Such systems have a limited number of final states and behave much like chemical engines.

Therefore, extending thermodynamic concepts to non-equilibrium systems can only provide an additional characterization of stationary states far from equilibrium, whereas the Location of these stationary states and the pathways to reach them are determined by kinetic equations.

As the system moves further from equilibrium, the magnitudes of X and J will increase, and the system may drift away from equilibrium, leaving the domain of linear thermodynamics without losing overall stability.

It is possible, however, that moving away from equilibrium triggers a bifurcation in the system, leading to instability. This gives rise to what is known as a thermodynamic fluctuation that drives the system away from the unstable point, which may cause the system to disintegrate.

Nevertheless, at certain parameter values, this fluctuation acts as a catalyst, steering the system toward a new state that inherits its stability. For example, The Emergence of a limit cycle or The formation of dissipative structures in distributed systems is also preceded by a breakdown of thermodynamic stability far from equilibrium.

Finally, transitions between stable stationary states occur at the boundary of stability, when the system undergoes an abrupt, jump-like transition between them.

Thus, the thermodynamic Criteria for the stability of stationary states coincide with the corresponding mathematical criteria and can serve as their supplementary characterization. However, far from equilibrium, there are no general thermodynamic criteria governing the direction of an open system's evolution, since its behavior is determined by dynamic properties and regulatory mechanisms rather than general statistical laws, as formulated in The Second Law of classical thermodynamics. This feature also accounts for The complexity of applying The concepts of entropy and information when describing the General Properties of biological systems.

METABOLISM/35.html">Selection/41.html">Review Questions and Exercises

1. Which Functions are referred to as Thermodynamic Potentials?

2. What is meant by the chemical potential of a given component?

3. What is the difference between chemical and electrochemical potentials?

4. What is the degree of advancement of a reaction?

5. Write down the definition of chemical affinity.

6. How is the sign of chemical affinity related to the direction of the reaction?

7. Why are the approaches of equilibrium thermodynamics inapplicable to the description of biological systems?

8. What are the advantages of switching to local variables when describing biological systems?

9. What are Generalized Forces and generalized flows?

10. How are generalized forces and generalized flows related in the thermodynamics of linear irreversible processes?

11. Write the law of conservation of mass in terms of the divergence of the matter flux.

12. Write the expression for the rate of local entropy production at a given point in the system in terms of generalized forces and generalized flows.

13. Give Examples of linear irreversible processes.

14. Write down the Onsager reciprocal relations.

15. Formulate the Curie-Prigogine principle.

16. State Prigogine's theorem.

17. Why does the Curie-Prigogine principle not hold for Biomembranes?

18. What state is referred to as a state of steady-state equilibrium?

19. What is the fundamental difference between Introduction/36.html">Biological Membranes and artificial non-biological semipermeable membranes?

20. Give an example of Flux Coupling in biomembranes.