Pressure and entropy of hard spheres in the weakly nonequilibrium heat-conduction steady state

TL;DR

This paper derives analytical expressions for pressure, internal energy, and entropy of hard spheres in a weakly nonequilibrium steady state with heat flux, across 1D, 2D, and 3D, confirming thermodynamic laws.

Contribution

It provides the first analytical formulas for thermodynamic quantities of hard spheres under small heat flux in various dimensions.

Findings

Gradient contributions to internal energy depend on volume

Entropy satisfies the second law of thermodynamics

Formulas derived for 1D, 2D, and 3D systems

Abstract

Thermodynamic quantities of the hard-sphere system in the steady state with a small heat flux are calculated within the continuous media approach. Analytical expressions for pressure, internal energy, and entropy are found in the approximation of the fourth order in temperature gradients. It is shown that the gradient contributions to the internal energy depend on the volume, while the entropy satisfies the second law of thermodynamics for nonequilibrium processes. The calculations are performed for dimensions 3D, 2D, and 1D.