# Global Thermodynamics for Heat Conduction Systems

## TL;DR

This paper introduces a new concept of global temperature for non-uniform heat conduction systems, extending thermodynamics to such systems and predicting interface temperature deviations and super-cooled gas formation.

## Contribution

It develops a global thermodynamics framework and a variational principle for phase coexistence in heat conduction systems, extending classical equilibrium concepts.

## Key findings

- Global temperature concept successfully extends thermodynamics.
- Predicts deviation of interface temperature from equilibrium.
- Identifies stable super-cooled gas near the interface.

## Abstract

We propose the concept of global temperature for spatially non-uniform heat conduction systems. With this novel quantity, we present an extended framework of thermodynamics for the whole system such that the fundamental relation of thermodynamics holds, which we call "global thermodynamics" for heat conduction systems. Associated with this global thermodynamics, we formulate a variational principle for determining thermodynamic properties of the liquid-gas phase coexistence in heat conduction, which corresponds to the natural extension of the Maxwell construction for equilibrium systems. We quantitatively predict that the temperature of the liquid-gas interface deviates from the equilibrium transition temperature. This result indicates that a super-cooled gas stably appears near the interface.