Thermodynamic-kinetic uncertainty relation: properties and an information-theoretic interpretation

TL;DR

This paper explores the thermodynamic-kinetic uncertainty relation (TKUR), demonstrating it as the tightest bound among similar inequalities and revealing its interpretation through information theory and Kullback-Leibler divergence.

Contribution

It shows that TKUR provides the tightest bounds on current precision and offers an information-theoretic interpretation involving Kullback-Leibler divergences.

Findings

TKUR is the tightest bound among a class of inequalities.

TKUR can be expressed as an inequality between two Kullback-Leibler divergences.

The divergence relates entropy production, dynamical activity, and current precision.

Abstract

Universal relations that characterize the fluctuations of nonequilibrium systems are of fundamental importance. The thermodynamic and kinetic uncertainty relations impose upper bounds on the precision of currents solely by total entropy production and dynamical activity, respectively. Recently, a tighter bound that imposes on the precision of currents by both total entropy production and dynamical activity has been derived (referred to as the TKUR). In this paper, we show that the TKUR gives the tightest bound of a class of inequalities that imposes an upper bound on the precision of currents by arbitrary functions of the entropy production, dynamical activity, and time interval. Furthermore, we show that the TKUR can be rewritten as an inequality between two Kullback-Leibler divergences. One comes from the ratio of entropy production to dynamical activity, the other comes from the Kullback-Leibler divergence between two probability distributions defined on two-element set, which are characterized by the ratio of precision of the time-integrated current to dynamical activity.