Current fluctuations in a particle-nonconserving reaction-diffusion process

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

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.

Effective stochastic generators for conditioned dynamics at an atypical reaction-diffusion current

We consider the fluctuations of a time-integrated particle current around an atypical value in a generic stochastic Markov process involving classical particles with two-site interaction and hard-core repulsion on a finite one-dimensional lattice with open boundaries. We address the question of which interactions one has to impose on such a process to make the atypical value of the current typical. It is known that a corresponding effective stochastic Markov process might exist whose typical current value is equal to the atypical current value in the original process within a time-translational invariant regime. This effective process has, in principle, nonlocal transition rates. Nevertheless, it turns out that under some conditions, the stochastic generator of the effective process has the same dynamical rules as the stochastic generator of the original process. We find these conditions and show that our approach can be generalized to any time-integrated observable.