Nonequilibrium Isothermal transformations in a temperature gradient from a microscopic dynamics
Letizia, Viviana; Olla, Stefano (2017), Nonequilibrium Isothermal transformations in a temperature gradient from a microscopic dynamics, Annals of Probability, 45, 6A, p. 39874018. 10.1214/16AOP1156
View/Open
Type
Article accepté pour publication ou publiéDate
2017Journal name
Annals of ProbabilityVolume
45Number
6APublisher
Institute of Mathematical Statistics
Pages
39874018
Publication identifier
Metadata
Show full item recordAbstract (EN)
We consider a chain of anharmonic oscillators immersed in a heat bath with a temperature gradient and a timevarying tension applied to one end of the chain while the other side is fixed to a point. We prove that under diffusive spacetime 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. 1. Introduction. Macroscopic isothermal thermodynamic transformations can be modeled microscopically by putting a system in contact with Langevin heat bath at a given temperature β −1. In [9] a chain of n anharmonic oscillators is immersed in a heat bath of Langevin thermostats acting independently on each particle. Macroscopically equivalent isothermal dynamics is obtained by elastic collisions with an external gas of independent particles with Maxwellian random velocities with variance β −1. The effect is to quickly renew the velocities distribution of the particles, so that at any given time it is very close to a maxwellian at given temperature. The chain is pinned only on one side, while at the opposite side a force (tension) τ is acting. The equilibrium distribution is characterized by the two control parameters β −1 , τ (temperature and tension). The total length and the energy of the system in equilibrium are in general nonlinear functions of these parameters given by the standard thermodynamic relations. By changing the tension τ applied to the system, a new equilibrium state, with the same temperature β −1 , will be eventually reached. For large n, while the heat bath equilibrates the velocities at the corresponding temperature at time of order 1, the system converges to this global equilibrium length at a time scale of order n 2 t. In [9] it is proven that the length stretch of the systemSubjects / Keywords
hypocoercivity; relative entropy; isothermal transformations; nonequilibrium stationary states; langevin heat bath; Hydrodynamic limitsRelated items
Showing items related by title and author.

Olla, Stefano (2014) Communication / Conférence

Komorowski, Tomasz; Olla, Stefano; Simon, Marielle (2020) Article accepté pour publication ou publié

Olla, Stefano (2010) Communication / Conférence

Olla, Stefano; Simon, Marielle (2015) Article accepté pour publication ou publié

Iacobucci, Alessandra; Olla, Stefano; Stoltz, Gabriel (2017) Article accepté pour publication ou publié