Heat transport in stochastic energy exchange models of locally confined hard spheres

TL;DR

This paper investigates heat transport in stochastic models of locally confined hard spheres, extending previous 2D results to 3D, and finds that heat conductivity correlates with energy exchange frequency, with simplified dynamics enabling faster simulations.

Contribution

It extends stochastic energy exchange models to three-dimensional hard spheres, providing a simpler kernel and confirming the relation between heat conductivity and exchange frequency.

Findings

Heat conductivity equals the energy exchange frequency.

The stochastic kernel is simpler, enabling faster computations.

Results extend previous 2D models to 3D dynamics.

Abstract

We study heat transport in a class of stochastic energy exchange systems that characterize the interactions of networks of locally trapped hard spheres under the assumption that neighbouring particles undergo rare binary collisions. Our results provide an extension to three-dimensional dynamics of previous ones applying to the dynamics of confined two-dimensional hard disks [Gaspard P & Gilbert T On the derivation of Fourier's law in stochastic energy exchange systems J Stat Mech (2008) P11021]. It is remarkable that the heat conductivity is here again given by the frequency of energy exchanges. Moreover the expression of the stochastic kernel which specifies the energy exchange dynamics is simpler in this case and therefore allows for faster and more extensive numerical computations.