The F-theorem for stochastic models
by R. F. Streater,
Annals of Phys., 218, 255-278, 1992.
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
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
© by Ray Streater, 13/6/00.