A hard disk analysis of momentum deficit due to dissipation

TL;DR

This paper investigates how dissipation causes a momentum deficit in nonequilibrium steady states of Brownian objects, using hard disk models and simulations to validate a general principle relating missing force to dissipation.

Contribution

It provides explicit analytical expressions and validation of the momentum deficit due to dissipation principle in hard disk gas models.

Findings

Analytical expressions for forces in hard disk models.

Validation of the momentum deficit principle through simulations.

Good agreement between theory and molecular dynamics results.

Abstract

When a Brownian object is in a nonequilibrium steady state, actual force exerted on it is different from one in a thermal equilibrium. In our previous paper [Phys. Rev. Lett. 108 (2012), 160601] we discovered a general principle which relates the missing force to dissipation rates through a concept of momentum deficit due to dissipation (MDD). In this article, we examine the principle using various models based on hard disk gases and Brownian pistons. Explicit expressions of the forces are obtained analytically and the results are compared with molecular dynamics simulations. The good agreement demonstrates the validity of MDD.