Hierarchical Reconstruction of Time-arrow from Multi-time Correlations

TL;DR

This paper introduces a hierarchical framework using multi-time correlations to estimate the entropy production rate in stochastic thermodynamics, providing progressively tighter bounds that converge to the true value with dense observations.

Contribution

It develops a systematic hierarchy of bounds on entropy production rate based on multi-time correlations, enabling improved experimental estimation of irreversibility.

Findings

Higher-order correlations yield tighter bounds on entropy production rate.

The hierarchy converges to the full entropy production rate with dense temporal sampling.

Abstract

The entropy production rate (EPR), a key measure of thermodynamic irreversibility in stochastic thermodynamics, is difficult to determine directly in experiments, motivating lower-bound-based estimation from observations. However, a systematic framework for organizing increasing amounts of the irreversibility information in experimental state observables into progressively tighter bounds remains lacking. Here, we show that multi-time correlations of a class of state observations naturally encode this information to provide a hierarchy. By defining a reconstruction operation as a combination of correlations, we obtain a sequence of lower bounds on the EPR. Correlations of higher order capture the thermodynamic information at greater temporal depth, thereby capturing more irreversibility and yielding tighter bounds. Under ideal conditions, this hierarchy converges to the full EPR in the limit of infinitely dense observations over a finite time window.