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).]
Cite
@article{arxiv.1908.03029,
title = {Stochastic order parameter dynamics for phase coexistence in heat conduction},
author = {Shin-ichi Sasa and Naoko Nakagawa and Masato Itami and Yohei Nakayama},
journal= {arXiv preprint arXiv:1908.03029},
year = {2021}
}
Comments
30 pages, 13 figures; In ver.2, the presentation has been substantially revised. 31 pages, 14 figures