Directed transport in equilibrium : analysis of the dimer model with inertial terms

TL;DR

This paper extends previous analysis of a dimer model in equilibrium by including inertial effects, deriving the Fokker-Planck equation, and exploring conditions for directed transport and possible oscillatory states.

Contribution

It introduces the full inertial model, derives the Fokker-Planck equation in this context, and analyzes velocity selection and equilibrium distributions.

Findings

Directed transport occurs in the inertial dimer model at equilibrium.

A uniformly translating equilibrium distribution is possible with inertial terms.

Potential for oscillatory non-equilibrium states within equilibrium is suggested.

Abstract

We have previously shown an analysis of our dimer model in the over-damped regime to show directed transport in equilibrium. Here we analyze the full model with inertial terms present to establish the same result. First we derive the Fokker-Planck equation for the system following a Galilean transformation to show that a uniformly translating equilibrium distribution is possible. Then, we find out the velocity selection for the centre of mass motion using that distribution on our model. We suggest generalization of our calculations for soft collision potentials and indicate to interesting situation with possibility of oscillatory non-equilibrium state within equilibrium.