Numerical examination of steady-state thermodynamics from the entropy connected to the excess heat

TL;DR

This paper numerically investigates the entropy in heat-conducting nonequilibrium states, confirming local equilibrium assumptions and exploring properties like extensivity and additivity, which impact thermodynamic analysis.

Contribution

The study introduces an efficient numerical method to estimate entropy from heat currents in nonequilibrium states, extending the applicability beyond local equilibrium assumptions.

Findings

Entropy agrees with local equilibrium hypothesis.

Entropy exhibits both extensivity and additivity.

Extensivity and additivity do not degenerate at nonequilibrium.

Abstract

We numerically determine the entropy for heat-conducting states, which is connected to the so-called excess heat considered as a basic quantity for steady-state thermodynamics in nonequilibrium. We adopt an efficient method to estimate the entropy from the bare heat current and find that the obtained entropy agrees with the familiar local equilibrium hypothesis well. Our method possesses a wider applicability than local equilibrium and opens a possibility to compare thermodynamic properties of complex systems with those in the local equilibrium. We further investigate the entropy for heat-conducting states and find that it exhibits both extensive and additive properties; however, the two properties do not degenerate each other differently from those at equilibrium. The separation of the extensivity and additivity makes it difficult to apply powerful thermodynamic methods.