Ultimate Kinetic Uncertainty Relation and Optimal Performance of Stochastic Clocks

TL;DR

This paper introduces a new, tighter bound on the uncertainty of stochastic fluxes in Markov processes, establishing optimal performance limits for stochastic clocks and extending results to semi-Markov and quantum processes.

Contribution

It derives the ultimate kinetic uncertainty relation, providing a tighter bound that can always be saturated, and characterizes the optimal performance of stochastic clocks, including quantum cases.

Findings

Derived a tighter uncertainty bound for Markov processes.

Established exact limits for first-passage time uncertainty.

Extended results to semi-Markov and quantum reset processes.

Abstract

For Markov processes over discrete configurations, an asymptotic bound on the uncertainty of stochastic fluxes is derived in terms of the harmonic mean of decay rates with respect to the stationary distribution. This bound is necessarily tighter than the bound in terms of the arithmetic mean, i.e., the activity, known as the kinetic uncertainty relation. What is more, it can always be saturated. In turn, an exact limit for the uncertainty of first-passage times as well as the optimal long-time performance of stochastic clocks are established. The results generalise to semi-Markov processes, including quantum reset processes, where it can be determined when clock performance improves thanks to coherent driving.