Dissipation bounds all steady-state current fluctuations

TL;DR

This paper proves that dissipation fundamentally constrains large current fluctuations in nonequilibrium systems, establishing bounds similar to linear response even far from equilibrium, and confirms a conjectured uncertainty relation.

Contribution

It introduces a linear-response-like bound on large deviation functions for currents in Markov jump processes, extending the understanding of fluctuation constraints far from equilibrium.

Findings

Large fluctuations are more probable than linear response predicts.

Dissipation bounds the structure of current fluctuations.

Confirms a conjectured uncertainty bound on current variance.

Abstract

Near equilibrium, small current fluctuations are described by a Gaussian with a linear-response variance regulated by the dissipation. Here, we demonstrate that dissipation still plays a dominant role in structuring large fluctuations arbitrarily far from equilibrium. In particular, we prove a linear-response-like bound on the large deviation function for currents in Markov jump processes. We find that nonequilibrium current fluctuations are always more likely than what is expected from a linear-response analysis. As a small-fluctuations corollary, we derive a recently-conjectured uncertainty bound on the variance of current fluctuations.