On the law of increase of entropy for nonequililbrium systems

TL;DR

This paper proves that the entropy of a nonequilibrium N-body system cannot decrease over time, establishing a lower bound and showing the entropy rate is non-negative, with applications to the BGK relaxation model.

Contribution

It provides a rigorous proof that nonequilibrium entropy has a lower bound and cannot decrease, extending the BGK model to a more general framework.

Findings

Entropy S has a lower bound and cannot decrease.

The rate of change of entropy dS/dt is non-negative.

A generalized BGK relaxation model is derived.

Abstract

Under the assumption of a smooth full phase-space distribution function we prove that the nonequilibrium entropy S which is considered as a functional of the distribution vector for an N-body system possesses a lower bound and therefore can not decrease. We also compute the rate of change of S, dS/dt, showing that this is non-negative and having a global minimum at equilibrium. As an aplication we obtain a generalization of the (Bhatnager-Gross-Krook) BGK relaxation model.