Mapping of uncertainty relations between continuous and discrete time

TL;DR

This paper compares current fluctuations in discrete and continuous-time Markov processes, establishing a mapping that simplifies deriving uncertainty bounds and reveals that continuous-time systems exhibit larger fluctuations due to transition timing randomness.

Contribution

It introduces a novel mapping between moments of currents in discrete and continuous-time processes, enabling unified uncertainty bounds derivation.

Findings

Continuous-time master equations have larger current fluctuations.

A mapping between discrete and continuous-time current moments is established.

New uncertainty bounds are derived from the mapping.

Abstract

Lower bounds on fluctuations of thermodynamic currents depend on the nature of time: discrete or continuous. To understand the physical reason, we compare current fluctuations in discrete-time Markov chains and continuous-time master equations. We prove that current fluctuations in the master equations are always more likely, due to random timings of transitions. This comparison leads to a mapping of the moments of a current between discrete and continuous time. We exploit this mapping to obtain new uncertainty bounds. Our results reduce the quests for uncertainty bounds in discrete and continuous time to a single problem.