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

Abstract

For continuous-time Markov jump processes on irreducible networks with 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 inequality that, similarly to the well-known Thermodynamic Uncertainty Relation (TUR), links the stationary entropy production rate with the fluctuations of an integrated current, but also incorporates the statistics of the forward and backward recurrence times. Such inequality can be saturated in less restrictive conditions than the TUR, and potentially offers new opportunities for the optimization and design of biological and chemical out-of-equilibrium systems at the nanoscale.