The Thermo-Kinetic Relations

TL;DR

This paper introduces a Thermo-Kinetic Relation that bounds entropy production in overdamped Markov jump processes, generalizing classical speed limits and thermodynamic uncertainty relations, with applications in biophysics and computing.

Contribution

It presents a new bound on entropy production for non-stationary and stationary Markov processes, extending thermodynamic uncertainty relations and speed limits.

Findings

Bound on entropy production involving absolute fluctuations.

Trade-off between non-adiabatic and housekeeping entropy production.

Constraints specific to constant-rate Markov processes.

Abstract

Thermo-Kinetic relations bound thermodynamic quantities such as entropy production with statistics of dynamical observables. We introduce a Thermo-Kinetic Relation to bound the entropy production or the non-adiabatic (Hatano-Sasa, excess) entropy production for overdamped Markov jump processes, possibly with time-varying rates and non stationary distributions. For stationary cases, this bound is akin to a Thermodynamic Uncertainty Relation, only involving absolute fluctuations rather than the mean square, thereby offering a better lower bound far from equilibrium. For non-stationary cases, this bound generalises Classical Speed Limits, where the kinetic term is not necessarily the activity (number of jumps) but any trajectory observable of interest. As a consequence, in the task of driving a system from a given probability distribution to another, we find a trade-off between non-adiabatic entropy production and housekeeping entropy production: the latter can be increased in order to decrease the former, although to a limited extent. We also find constraints specific to constant-rate Markov processes. We illustrate our Thermo-Kinetic Relations on simple examples from biophysics and computing devices.