The F-theorem for stochastic models, by R. F. Streater; free energy, convexity, Legendre transforms, Lyapunov function, entropy

The F-theorem for stochastic models

by R. F. Streater,

Annals of Phys., 218, 255-278, 1992.

ABSTRACT

Heat variables are added to the stochastic models, that is, discrete systems obeying a non-linear time-evolution called the discrete Boltzmann equation. When the evolution is modified so that the heat variables remain fixed at a given temperature, the H-theorem of the isolated system becomes the F-theorem of the closed system: the free energy F is monotone decreasing along the orbit. This is used to show that a large family of chemical rate equations converge to equilibrium, including the Ising model with Glauber dynamics. Some changes in certain commonly used equations are suggested, making them compatible with the general scheme.

REMARKS

This theory has been developed in my book. It shows that a meaning can be given to free energy under isothermal conditions, even when the system is not in equilibrium. The free energy is a decreasing function of time.

Go to my HOME PAGE for links to all my papers on mathematical physics, or to my recent papers for work on statistical dynamics.