Asymptotics of work distributions: The pre-exponential factor

TL;DR

This paper derives the full asymptotic form of work distributions in driven Langevin systems, emphasizing the pre-exponential factor for parameter-free results, and confirms findings with simulations, including a universal form for parabolic potentials.

Contribution

It provides a complete asymptotic analysis of work distributions, focusing on the pre-exponential factor, and introduces a universal form for certain potentials.

Findings

Accurate asymptotic expressions for work distributions

Pre-exponential factor calculation without adjustable parameters

Universal form for parabolic potential work distributions

Abstract

We determine the complete asymptotic behaviour of the work distribution in driven stochastic systems described by Langevin equations. Special emphasis is put on the calculation of the pre-exponential factor which makes the result free of adjustable parameters. The method is applied to various examples and excellent agreement with numerical simulations is demonstrated. For the special case of parabolic potentials with time-dependent frequencies, we derive a universal functional form for the asymptotic work distribution.