Hyperaccurate bounds in discrete-state Markovian systems

TL;DR

This paper derives a precise expression for the least fluctuating thermodynamic current in discrete-state Markov systems, showing it provides tighter bounds than traditional TURs and has implications for estimating entropy production.

Contribution

It introduces a closed-form hyperaccurate current for Markov systems, offering tighter bounds than TURs and new bounds for work converter efficiency, with applications to biological and chemical models.

Findings

Hyperaccurate current has minimal fluctuations in Markov systems.

Hyperaccurate bounds outperform traditional TUR bounds.

Applications demonstrate relevance to biological and chemical systems.

Abstract

Generalized empirical currents represent a vast class of thermodynamic observables of mesoscopic systems. Their fluctuations satisfy the thermodynamic uncertainty relations (TURs), as they can be bounded by the average entropy production. Here, we derive a general closed expression for the hyperaccurate current in discrete-state Markovian systems, i.e., the one with the least fluctuations, for both discrete- and continuous-time evolution. We show that its associated hyperaccurate bound is generally much tighter than the one given by the TURs, and might be crucial to providing a reliable estimation of the average entropy production. We also show that one-loop systems (rings) exhibit a hyperaccurate current only for finite times, highlighting the importance of short-time observations. Additionally, we derive two novel bounds for the efficiency of work-to-work converters, solely as a function of either the input or the output power. Finally, our theoretical results are employed to analyze a 6-state model network for kinesin, and a chemical system in a thermal gradient exhibiting a dissipation-driven selection of states.