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November 2017 Nonequilibrium isothermal transformations in a temperature gradient from a microscopic dynamics
Viviana Letizia, Stefano Olla
Ann. Probab. 45(6A): 3987-4018 (November 2017). DOI: 10.1214/16-AOP1156


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.


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Viviana Letizia. Stefano Olla. "Nonequilibrium isothermal transformations in a temperature gradient from a microscopic dynamics." Ann. Probab. 45 (6A) 3987 - 4018, November 2017.


Received: 1 May 2015; Revised: 1 May 2016; Published: November 2017
First available in Project Euclid: 27 November 2017

zbMATH: 06838113
MathSciNet: MR3729621
Digital Object Identifier: 10.1214/16-AOP1156

Primary: 60K35
Secondary: 35Q79 , 82C05 , 82C22

Keywords: Hydrodynamic limits , hypocoercivity , isothermal transformations , Langevin heat bath , non-equilibrium stationary states , Relative entropy

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.45 • No. 6A • November 2017
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