Short-time fluctuations of displacements and work

TL;DR

This paper discusses a theorem on short-time particle displacement fluctuations, explores a series expansion for work fluctuation distributions, and presents numerical results indicating the expansion's validity up to about a picosecond in a Lennard-Jones fluid.

Contribution

It introduces a series expansion for work fluctuations based on a recent theorem and evaluates its convergence time scale through numerical simulations.

Findings

Series expansion converges up to approximately one picosecond.

Gaussian distribution suffices for displacements below this time scale.

Numerical results support the theoretical short-time behavior analysis.

Abstract

A recent theorem giving the initial behavior of very short-time fluctuations of particle displacements in classical many-body systems is discussed. It has applications to equilibrium and non-equilibrium systems, one of which is a series expansion of the distribution of work fluctuations around a Gaussian function. To determine the time-scale at which this series expansion is valid, we present preliminary numerical results for a Lennard-Jones fluid. These results suggest that the series expansion converges up to time scales on the order of a picosecond, below which a simple Gaussian function for the distribution of the displacements can be used.