On asymptotic behavior of work distributions for driven Brownian motion

TL;DR

This paper proposes a conjecture for the asymptotic form of work distributions in driven overdamped Brownian motion, supported by simulations and theory, and introduces new analytical solutions for specific potentials.

Contribution

It introduces a simple conjecture for the asymptotic behavior of work distributions, validated for certain potentials, and extends EN theory to nonequilibrium initial conditions.

Findings

Conjecture holds for potentials with confinement equal or weaker than parabolic.

New analytical solution for V-potential work distribution.

Extended EN theory to nonequilibrium initial positions.

Abstract

We propose a simple conjecture for the functional form of the asymptotic behavior of work distributions for driven overdamped Brownian motion of a particle in confining potentials. This conjecture is motivated by the fact that these functional forms are independent of the velocity of the driving for all potentials and protocols, where explicit analytical solutions for the work distributions have been derived in the literature. To test the conjecture, we use Brownian dynamics simulations and a recent theory developed by Engel and Nickelsen (EN theory), which is based on the contraction principle of large deviation theory. Our tests suggest that the conjecture is valid for potentials with a confinement equal to or weaker than the parabolic one, both for equilibrium and for nonequilibrium distributions of the initial particle position. In addition we obtain a new analytical solution for the asymptotic behavior of the work distribution for the V-potential by application of the EN theory, and we extend this theory to nonequilibrated initial particle positions.