Spatial correlations in nonequilibrium reaction-diffusion problems by the Gillespie algorithm

TL;DR

This paper investigates spatial correlations in a one-dimensional reaction-diffusion system using Gillespie algorithm simulations, revealing short-range correlations at equilibrium and long-range out of equilibrium, consistent with fluctuating hydrodynamics.

Contribution

It applies the Gillespie algorithm to study spatial correlations in reaction-diffusion systems, confirming theoretical predictions for nonequilibrium behavior.

Findings

Correlations are short-ranged at equilibrium.

Correlations become long-ranged out of equilibrium.

Results agree with fluctuating hydrodynamics theory.

Abstract

We present a study of the spatial correlation functions of a one-dimensional reaction-diffusion system in both equilibrium and out of equilibrium. For the numerical simulations we have employed the Gillespie algorithm dividing the system in cells to treat diffusion as a chemical process between adjacent cells. We find that the spatial correlations are spatially short ranged in equilibrium but become long ranged in nonequilibrium. These results are in good agreement with theoretical predictions from fluctuating hydrodynamics for a one-dimensional system and periodic boundary conditions.