Approach to a non-equilibrium steady state

TL;DR

This paper models a non-interacting gas under a constant external field, analyzing its approach to a non-equilibrium steady state through kinetic theory, revealing diffusion behavior and validating a generalized Green-Kubo relation.

Contribution

It introduces an analytical calculation of the diffusion coefficient in a non-equilibrium steady state and extends the Green-Kubo formula to this context.

Findings

Diffusion coefficient exhibits a minimum at intermediate field strengths.

The approach to steady state is dominated by hydrodynamic diffusion and convection.

Green-Kubo formula is valid in the non-equilibrium stationary state.

Abstract

We consider a non-interacting one-dimensional gas accelerated by a constant and uniform external field. The energy absorbed from the field is transferred via elastic collisions to a bath of scattering obstacles. At gas-obstacle encounters the particles of the gas acquire a fixed kinetic energy. The approach to the resulting stationary state is studied within the Boltzmann kinetic theory. It is shown that the long time behavior is governed by the hydrodynamic mode of diffusion superposed on a convective flow. The diffusion coefficient is analytically calculated for any value of the field showing a minimum at intermediate field intensities. It is checked that the properly generalized Green-Kubo formula applies in the non-equilibrium stationary state.