The free-energy theorem

by R. F. Streater, in "Quantum and non-commutative analysis", Eds. H. Araki, K. R. Ito, A. Kishimoto, and I. Ojima, 1993. pp 137-147; Kluwer.

ABSTRACT

We explain what goes into the proof of the free-energy theorem, which says that in the non-equilibrium dynamics of a system in contact with a heat-bath in a Gibbs state at a given temperature T, the free energy F=E-TS is a decreasing function of time and reaches its minimum at thermal equilibrium. Here, E is the internal energy and S is the entropy. The method is a simplification of the original research, to be found in The F-theorem for stochastic models.

This shows that, within statistical dynamics, a meaning can be given to the free-energy under isothermal conditions, when the system is not in equilibrium. This free energy is a decreasing function of time.