Well-posedness of stochastic reacting particle systems with non-local and Lennard-Jones interactions

TL;DR

This paper proves the well-posedness of stochastic particle systems with Lennard-Jones interactions and non-local fields, extending to reaction models relevant for cultural heritage material sulphation.

Contribution

It introduces a novel analysis for stochastic particle systems with singular Lennard-Jones interactions and coupled nonlocal fields, including reaction dynamics.

Findings

Established well-posedness for systems with Lennard-Jones interactions.

Extended analysis to reaction models with field-dependent switching rates.

Developed an interlacing technique for full system well-posedness.

Abstract

We establish well-posedness results for systems of a finite number of stochastic particles driven by independent Brownian motions and subject to a strongly singular drift induced by a Lennard-Jones interaction. In addition to the pairwise force, the dynamics includes a nonlocal drift mediated by an environmental field, whose evolution is coupled to the particle configuration through a regularized empirical density. We then extend the analysis to a reaction model in which the switching (or killing) rate also depends on the field. An interlacing technique is considered for establishing the well-posedness of the full system. The model is motivated by the challenge to provide a stochastic microscopic description of the sulphation phenomenon in cultural heritage materials.