Analytic calculation of energy transfer and heat flux in a one-dimensional system

TL;DR

This paper provides an analytical approach to calculating energy transfer and heat flux in a one-dimensional gas, clarifying the contributions of mechanical work and heat conduction, and analyzing the Fourier law in this context.

Contribution

It introduces an analytical method for calculating energy transfer and heat flux in a one-dimensional gas, distinguishing mechanical work from heat conduction contributions.

Findings

Derived a formula for steady-state energy flux.

Separated mechanical work and heat conduction contributions.

Analyzed the nonlinear dependence of mechanical work on drift velocity.

Abstract

In the context of the problem of heat conduction in one-dimensional systems, we present an analytical calculation of the instantaneous energy transfer across a tagged particle in a one-dimensional gas of equal-mass, hard-point particles. From this, we obtain a formula for the steady-state energy flux, and identify and separate the mechanical work and heat conduction contributions to it. The nature of the Fourier law for the model, and the nonlinear dependence of the rate of mechanical work on the stationary drift velocity of the tagged particle, are analyzed and elucidated.