Affinity- and topology-dependent bound on current fluctuations

TL;DR

This paper proves a universal bound on current fluctuations in Markovian processes, linking fluctuations to cycle affinities and network topology, with refinements for equilibrium and locally vanishing affinities.

Contribution

It provides a rigorous proof of a conjectured bound connecting current fluctuations, cycle affinities, and network topology in Markov processes.

Findings

Established a universal bound on current fluctuations

Linked fluctuations to cycle affinities and network topology

Refined the bound for equilibrium and locally vanishing affinities

Abstract

We provide a proof of a recently conjectured universal bound on current fluctuations in Markovian processes. This bound establishes a link between the fluctuations of an individual observable current, the cycle affinities driving the system into a non-equilibrium steady state, and the topology of the network. The proof is based on a decomposition of the network into independent cycles with both positive affinity and positive stationary cycle current. This formalism allows for a refinement of the bound for systems in equilibrium or with locally vanishing affinities.