Unique extension of the maximum entropy principle to phase coexistence in heat conduction

TL;DR

This paper extends the maximum entropy principle to describe phase coexistence in heat conduction, providing a new variational approach to analyze thermodynamic variables in steady states with liquid-gas interfaces.

Contribution

It introduces a unique extension of the maximum entropy principle applicable to phase coexistence in heat conduction, under specific thermodynamic assumptions.

Findings

The extended variational principle is unique under given conditions.

The temperature at the liquid-gas interface deviates from the equilibrium transition temperature.

Predictions can be verified through experiments.

Abstract

The maximum entropy principle determines the values of thermodynamic variables in thermally isolated equilibrium systems. This paper extends the principle to a variational principle that applies to liquid-gas coexistence in heat conduction. We show the uniqueness of the extension under the assumption that the variational principle and the fundamental thermodynamic relation are simultaneously extended in the linear response regime with the total energy fixed. Using the extended variational principle, we calculate the thermodynamic quantities in this steady state and find that the temperature of the liquid-gas interface deviates from the equilibrium transition temperature, which should be verified in experiments.