Heat flow in a periodically forced, thermostatted chain

TL;DR

This paper studies heat flow in a harmonic chain with thermal contact and periodic forcing, demonstrating finite heat conductivity, approach to a periodic state, and deriving a macroscopic temperature profile from microscopic dynamics.

Contribution

It proves the system's convergence to a time periodic state and derives a continuum heat equation describing the macroscopic temperature profile.

Findings

Finite heat conductivity due to velocity reversal actions.

System approaches a time periodic state with finite heat current.

Macroscopic temperature profile matches a continuum heat equation.

Abstract

We investigate the properties of a harmonic chain in contact with a thermal bath at one end and subjected, at its other end, to a periodic force. The particles also undergo a random velocity reversal action, which results in a finite heat conductivity of the system. We prove the approach of the system to a time periodic state and compute the heat current, equal to the time averaged work done on the system, in that state. This work approaches a finite positive value as the length of the chain increases. Rescaling space, the strength and/or the period of the force leads to a macroscopic temperature profile corresponding to the stationary solution of a continuum heat equation with Dirichlet-Neumann boundary conditions.