Thermodynamic Variational Principle Unifying Gravity and Heat Flow

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.

7 pages, 4 figures