Thermodynamic Variational Principle Unifying Gravity and Heat Flow

TL;DR

This paper introduces a variational principle within extended thermodynamics that unifies gravity and heat flow effects into an effective gravity parameter, enabling prediction of stable phase configurations in non-equilibrium liquid-gas systems.

Contribution

It proposes a novel global thermodynamics framework that unifies gravity and heat flow effects into an effective gravity parameter for phase configuration prediction.

Findings

Effective gravity determines phase stability.

Liquid at bottom if effective gravity is positive.

Predicts phase arrangement in non-equilibrium systems.

Abstract

Predicting the stable phase configuration in a liquid-gas system becomes a fundamental challenge when the stratification favored by gravity conflicts with arrangements induced by heat flow, particularly because standard equilibrium thermodynamics is insufficient in such non-equilibrium steady states. We propose a variational principle based on an extended thermodynamics, called global thermodynamics, to address this state selection problem. Our key finding is that gravity and heat flow effects are unified into a single parameter, ``effective gravity'' ($g_\mathrm{eff}$), within this framework. Crucially, the sign of $g_\mathrm{eff}$ determines the stable configuration: liquid is at the bottom if $g_\mathrm{eff} > 0$, and floats above the gas if $g_\mathrm{eff} < 0$. This provides a quantitative tool for the configuration prediction under competing drives.