Large deviation function and fluctuation theorem for classical particle transport

TL;DR

This paper analytically derives the large deviation function for classical particle transfer between reservoirs, demonstrating conditions under which the fluctuation theorem holds and analyzing the approach to steady state.

Contribution

It provides an analytical evaluation of the large deviation function and clarifies the conditions for the fluctuation theorem in a simple particle transfer model.

Findings

Steady state fluctuation theorem holds under certain decay conditions of particle number distribution.

The large deviation function is explicitly evaluated for a simple classical transfer model.

Conditions for the analyticity of the generating function are identified.

Abstract

We analytically evaluate the large deviation function in a simple model of classical particle transfer between two reservoirs. We illustrate how the asymptotic large time regime is reached starting from a special propagating initial condition. We show that the steady state fluctuation theorem holds provided that the distribution of the particle number decays faster than an exponential, implying analyticity of the generating function and a discrete spectrum for its evolution operator.