Current fluctuations and statistics during a large deviation event in an exactly solvabletransport model

Abstract

We study the distribution of the time-integrated current in an exactly solvable toy model ofheat conduction, both analytically and numerically. The simplicity of the model allowsus to derive the full current large deviation function and the system statisticsduring a large deviation event. In this way we unveil a relation between systemstatistics at the end of a large deviation event and for intermediate times. Themid-time statistics is independent of the sign of the current, a reflection of thetime-reversal symmetry of microscopic dynamics, while the end-time statistics doesdepend on the current sign, and also on its microscopic definition. We compare ourexact results with simulations based on the direct evaluation of large deviationfunctions, analyzing the finite-size corrections of this simulation method and derivingdetailed bounds for its applicability. We also show how the Gallavotti–Cohenfluctuation theorem can be used to determine the range of validity of simulationresults.