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.
Highlights
The behavior of liquids and gases close to equilibrium have been extensively studied for a long time
A = d3r a(T (r), p(r))ρ(r) = a(T, p)N + O(ε2). This indicates that all global thermodynamic quantities are equivalent to those in equilibrium by adopting the global temperature Tin (10.1), and that global thermodynamics for heat conduction systems are generally mapped to equilibrium thermodynamics, regardless of the shape of the container
We have developed a thermodynamic framework for heat conduction states, which we call global thermodynamics
Summary
The behavior of liquids and gases close to equilibrium have been extensively studied for a long time. In this paper, we construct a new universal theory for thermodynamic properties in the linear response regime. A new concept, global temperature, is found, with which a novel framework of global thermodynamics is constructed to describe the whole of non-uniform non-equilibrium systems with local equilibrium thermodynamics. This outcome provides a fresh viewpoint for the description of systems out of equilibrium. In the remaining part of this introduction, we first present a brief summary of development in non-equilibrium statistical mechanics, confirming that the phenomenon described above has never been discussed by established theories. At the end of the introduction, we summarize the achievements of this paper
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