NONEQUILIBRIUM ISOTHERMAL TRANSFORMATIONS IN A TEMPERATURE GRADIENT FROM A MICROSCOPIC DYNAMICS

• 成果类型: Article
• 署名作者: Letizia, Viviana; Olla, Stefano
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1156
• 发表日期: 2017
• 页码: 3987-4018
• 关键词: ornstein-uhlenbeck particles; ginzburg-landau models; hydrodynamic limit; hamiltonian system; fluctuations; noise

摘要

We consider a chain of anharmonic oscillators immersed in a heat bath with a temperature gradient and a time-varying tension applied to one end of the chain while the other side is fixed to a point. We prove that under diffusive space-time rescaling the volume strain distribution of the chain evolves following a nonlinear diffusive equation. The stationary states of the dynamics are of nonequilibrium and have a positive entropy production, so the classical relative entropy methods cannot be used. We develop new estimates based on entropic hypocoercivity, that allow to control the distribution of the position configurations of the chain. The macroscopic limit can be used to model isothermal thermodynamic transformations between nonequilibrium stationary states.