Characterizing steady state and transient properties of reaction-diffusion systems

TL;DR

This paper investigates the steady state and transient behaviors of reaction-diffusion systems, especially focusing on systems lacking microscopic reversibility, by analyzing a specific observable that obeys fluctuation relations.

Contribution

It introduces a novel observable for reaction-diffusion systems that remains well-defined without microscopic reversibility and obeys fluctuation relations, enabling analysis of transient properties.

Findings

Transient fluctuation ratios reveal peculiarities in configuration space trajectories.

The observable obeys an exact detailed fluctuation relation when detailed balance holds.

Microscopic dynamics influence the features observed in fluctuation ratios.

Abstract

In the past the study of reaction-diffusion systems has greatly contributed to our understanding of the behavior of many-body systems far from equilibrium. In this paper we aim at characterizing the properties of diffusion limited reactions both in their steady states and out of stationarity. Many reaction-diffusion systems have the peculiarity that microscopic reversibility is broken such that their transient behavior can not be investigated through the study of most of the observables discussed in the literature. For this reason we analyze the transient properties of reaction-diffusion systems through a specific work observable that remains well defined even in the absence of microscopic reversibility and that obeys an exact detailed fluctuation relation in cases where detailed balance is fulfilled. We thereby drive the systems out of their nonequilibrium steady states through time-dependent reaction rates. Using a numerical exact method and computer simulations, we analyze fluctuation ratios of the probability distributions obtained during the forward and reversed processes. We show that the underlying microscopic dynamics gives rise to peculiarities in the configuration space trajectories, thereby yielding prominent features in the fluctuation ratios.