Uncovering nonequilibrium from unresolved events

TL;DR

This paper introduces model-free methods to detect nonequilibrium states and estimate entropy production from unresolved multifilar events in complex systems, relaxing previous assumptions and applicable across various regimes.

Contribution

It extends existing frameworks by assessing non-Markovian statistics of multifilar events, enabling detection and quantification of nonequilibrium behavior without detailed system models.

Findings

Developed asymmetry-based tools for nonequilibrium detection

Provided bounds and estimates for entropy production

Validated methods through analytical and numerical models

Abstract

Closely related to the laws of thermodynamics, the detection and quantification of disequilibria are crucial in unraveling the complexities of nature, particularly those beneath observable layers. Theoretical developments in nonequilibrium thermodynamics employ coarse-graining methods to consider a diversity of partial information scenarios that mimic experimental limitations, allowing the inference of properties such as the entropy production rate. A ubiquitous but rather unexplored scenario involves observing events that can possibly arise from many transitions in the underlying Markov process--which we dub $\textit{multifilar events}$--as in the cases of exchanges measured at particle reservoirs, hidden Markov models, mixed chemical and mechanical transformations in biological function, composite systems, and more. We relax one of the main assumptions in a previously developed framework, based on first-passage problems, to assess the non-Markovian statistics of mutifilar events. By using the asymmetry of event distributions and their waiting-times, we put forward model-free tools to detect nonequilibrium behavior and estimate entropy production, while discussing their suitability for different classes of systems and regimes where they provide no new information, evidence of nonequilibrium, a lower bound for entropy production, or even its exact value. The results are illustrated in reference models through analytics and numerics.