Enantiodromic effective generators of a Markov jump process with Gallavotti-Cohen symmetry

TL;DR

This paper investigates the symmetry properties of stochastic generators in Markov jump processes, revealing enantiodromic relations between effective processes biased by conjugate fields, exemplified through a solvable particle creation-annihilation model.

Contribution

It introduces the concept of enantiodromic generators in Markov processes with Gallavotti-Cohen symmetry, providing a novel understanding of their structure and relations.

Findings

Effective generators with bias fields s and E-s are enantiodromic.

Theoretical framework established for symmetry properties of biased Markov processes.

Illustration through an exactly solvable particle creation-annihilation model.

Abstract

This paper deals with the properties of the stochastic generators of the effective (driven) processes associated with atypical values of transition-dependent time-integrated currents with Gallavotti-Cohen symmetry in Markov jump processes. Exploiting the concept of biased ensemble of trajectories by introducing a biasing field $s$, we show that the stochastic generators of the effective processes associated with the biasing fields $s$ and $E-s$ are enantiodromic with respect to each other where $E$ is the conjugated field to the current. We illustrate our findings by considering an exactly solvable creation-annihilation process of classical particles with nearest-neighbor interactions defined on a one-dimensional lattice.