Local entropy of a nonequilibrium fermion system

TL;DR

This paper investigates the local entropy of nonequilibrium fermion systems, establishing thermodynamic relations, inequalities, and the maximum entropy principle, and confirming consistency with the third law of thermodynamics.

Contribution

It provides a detailed analysis of local entropy in nonequilibrium fermion systems, deriving thermodynamic laws and principles applicable to such systems.

Findings

Local temperature and chemical potential relate to derivatives of local entropy.

The first law leads to an inequality for local entropy change.

Maximum entropy principle is proven for nonequilibrium distributions.

Abstract

The local entropy of a nonequilibrium system of independent fermions is investigated, and analyzed in the context of the laws of thermodynamics. It is shown that the local temperature and chemical potential can only be expressed in terms of derivatives of the local entropy for linear deviations from local equilibrium. The first law of thermodynamics is shown to lead to an inequality, not an equality, for the change in the local entropy as the nonequilibrium state of the system is changed. The maximum entropy principle (second law of thermodynamics) is proven: a nonequilibrium distribution has a local entropy less than or equal to a local equilibrium distribution satisfying the same constraints. It is shown that the local entropy of the system tends to zero when the local temperature tends to zero, consistent with the third law of thermodynamics.