Universal tradeoff relation between speed, uncertainty, and dissipation in nonequilibrium stationary states

TL;DR

This paper establishes universal thermodynamic inequalities that connect speed, uncertainty, and dissipation in nonequilibrium stationary states, revealing fundamental limits on stochastic current processes.

Contribution

It derives universal bounds on moments of first-passage times in nonequilibrium Markov processes, linking thermodynamics with stochastic process timing.

Findings

Lower bounds on mean first-passage times near equilibrium follow Van't Hoff-Arrhenius law.

Universal speed limits are established for rate processes far from equilibrium.

When the current is entropy production, the bounds become equalities due to martingale properties.

Abstract

We derive universal thermodynamic inequalities that bound from below the moments of first-passage times of stochastic currents in nonequilibrium stationary states of Markov jump processes in the limit where the thresholds that define the first-passage problem are large. These inequalities describe a tradeoff between speed, uncertainty, and dissipation in nonequilibrium processes, which are quantified, respectively, with the moments of the first-passage times of stochastic currents, the splitting probability, and the mean entropy production rate. Near equilibrium, the inequalities imply that mean first-passage times are lower bounded by the Van't Hoff-Arrhenius law, whereas far from thermal equilibrium the bounds describe a universal speed limit for rate processes. When the current is the stochastic entropy production, then the bounds are equalities, a remarkable property that follows from the fact that the exponentiated negative entropy production is a martingale.