Using precision coefficients on recurrence times and integrated currents to lower bound the average dissipation rate

TL;DR

This paper introduces a refined lower bound for the entropy production rate in Markov jump processes by incorporating recurrence times and integrated currents, extending the Thermodynamic Uncertainty Relation to improve accuracy far from equilibrium.

Contribution

It develops a new bound for entropy production that includes recurrence time statistics, enhancing the TUR for out-of-equilibrium systems.

Findings

The augmented TUR is tighter than the standard TUR far from equilibrium.

Incorporating recurrence times improves bounds on dissipation.

Potential applications in optimizing nanoscale biological and chemical systems.

Abstract

For continuous-time Markov jump processes on irreducible networks and time-independent rate constants, we employ a transition-based formalism to express the long-time precision of a single integrated current over an observable channel in terms of precisions of the recurrence times of the forward and backward jumps, and of an effective affinity that captures the thermodynamic driving on that channel. This leads to a general lower bound for the stationary entropy production rate that extends the well-known Thermodynamic Uncertainty Relation (TUR). Such an augmented TUR, which incorporates the statistics of the recurrences, proves to be tighter than the standard one far from equilibrium, and potentially offers new opportunities for the optimization and design of biological and chemical out-of-equilibrium systems at the nanoscale.