Inferring dissipation from current fluctuations

TL;DR

This paper derives and extends inequalities linking current fluctuations to dissipation in Markov jump and diffusion processes, enabling dissipation inference from coarse-grained observations.

Contribution

It rederives a dissipation-fluctuation inequality, adapts it to diffusion processes, and analyzes how spatial coarse-graining affects dissipation estimation.

Findings

Diffusions saturate the fluctuation-dissipation inequality.

Coarse-grained current fluctuations can bound total dissipation.

Bound tightness depends on detection of large thermodynamic forces.

Abstract

Complex physical dynamics can often be modeled as a Markov jump process between mesoscopic configurations. When jumps between mesoscopic states are mediated by thermodynamic reservoirs, the time-irreversibility of the jump process is a measure of the physical dissipation. We rederive a recently introduced inequality relating the dissipation rate to current fluctuations in jump processes. We then adapt these results to diffusion processes via a limiting procedure, reaffirming that diffusions saturate the inequality. Finally, we study the impact of spatial coarse-graining in a two-dimensional model with driven diffusion. By observing fluctuations in coarse-grained currents, it is possible to infer a lower bound on the total dissipation rate, including the dissipation associated with hidden dynamics. The tightness of this bound depends on how well the spatial coarse-graining detects dynamical events that are driven by large thermodynamic forces.