Stochastic order parameter dynamics for phase coexistence in heat conduction

Abstract

We propose a stochastic order parameter equation for describing phase coexistence in steady heat conduction near equilibrium. By analyzing the stochastic dynamics with a non-equilibrium adiabatic boundary condition, where total energy is conserved over time, we derive a variational principle that determines thermodynamic properties in non-equilibrium steady states. The resulting variational principle indicates that the temperature of the interface between the ordered region and the disordered region becomes greater (less) than the equilibrium transition temperature in the linear response regime when the thermal conductivity in the ordered region is less (greater) than that in the disordered region. This means that a super-heated ordered (super-cooled disordered) state appears near the interface, which was predicted by an extended framework of thermodynamics proposed in [N. Nakagawa and S.-i. Sasa, Liquid-gas transitions in steady heat conduction, Phys. Rev. Lett. {\bf 119}, 260602, (2017).]

arXiv comment30 pages, 13 figures; In ver.2, the presentation has been substantially revised. 31 pages, 14 figures

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Cited by in corpus (7)

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• Global Thermodynamics for Heat Conduction Systems
• Unique extension of the maximum entropy principle to phase coexistence in heat conduction
• Non-equilibrium coexistence between a fluid and a hotter or colder crystal of granular hard disks
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• Phase coexistence in a weakly stochastic reaction-diffusion system
• Thermodynamics of stationary states of the ideal gas in a heat flow