Kinetic uncertainty relation

TL;DR

This paper introduces a kinetic uncertainty relation that bounds fluctuations of observables in stochastic systems using the mean number of jumps, providing a new perspective distinct from thermodynamic uncertainty relations.

Contribution

It presents a novel kinetic uncertainty relation applicable to Markov jump systems, highlighting its importance far from equilibrium and contrasting it with thermodynamic constraints.

Findings

Kinetic uncertainty relation bounds fluctuations using mean jumps.

The relation is more relevant far from equilibrium.

Application to molecular motors and predator-prey dynamics.

Abstract

Relative fluctuations of observables in discrete stochastic systems are bounded at all times by the mean dynamical activity in the system, quantified by the mean number of jumps. This constitutes a kinetic uncertainty relation that is fundamentally different from the thermodynamic uncertainty relation recently discussed in the literature. The thermodynamic constraint is more relevant close to equilibrium while the kinetic constraint is the limiting factor of the precision of a observables in regimes far from equilibrium. This is visualized for paradigmatic simple systems and with an example of molecular motor dynamics. Our approach is based on the recent fluctuation response inequality by Dechant and Sasa [arXiv:1804.08250] and can be applied to generic Markov jump systems, which describe a wide class of phenomena and observables, including the irreversible predator-prey dynamics that we use as an illustration.