Open reactiondiffusion systems: bridging probabilistic theory across scales
Abstract
Reactiondiffusion processes are the foundational model for a diverse range of complex systems, ranging from biochemical reactions to social agentbased phenomena. The underlying dynamics of these systems occur at the individual particle/agent level, and in realistic applications, they often display interaction with their environment through energy or material exchange with a reservoir. This requires intricate mathematical considerations, especially in the case of material exchange since the varying number of particles/agents results in ``onthefly'' modification of the system dimension. In this work, we first overview the probabilistic description of reactiondiffusion processes at the particle level, which readily handles varying numbers of particles. We then extend this model to consistently incorporate interactions with macroscopic material reservoirs. Based on the resulting expressions, we bridge the probabilistic description with macroscopic concentrationbased descriptions for linear and nonlinear reactiondiffusion systems, as well as for an archetypal open reactiondiffusion system. This establishes a methodological workflow to bridge particlebased probabilistic descriptions with macroscopic concentrationbased descriptions of reactiondiffusion in open settings, laying the foundations for a multiscale theoretical framework upon which to construct theory and simulation schemes that are consistent across scales.
 Publication:

arXiv eprints
 Pub Date:
 April 2024
 DOI:
 10.48550/arXiv.2404.07119
 arXiv:
 arXiv:2404.07119
 Bibcode:
 2024arXiv240407119D
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Mathematical Physics;
 Physics  Chemical Physics;
 Quantitative Biology  Quantitative Methods;
 82Dxx;
 8210;
 9210;
 60Gxx;
 37N05;
 65Pxx;
 6008;
 J.2;
 J.3;
 G.3