Modeling multi-particle complexes in stochastic chemical systems

TL;DR

This paper introduces a Fock space framework and diagrammatic methods to model and analyze multi-particle complexes in stochastic chemical systems, simplifying the equations and providing a systematic approach.

Contribution

It presents a novel Fock space structure and diagrammatic techniques for describing complex particle assemblies in stochastic systems, bridging a gap in mathematical modeling.

Findings

Simplifies equations for equilibrium and non-equilibrium systems

Establishes a mathematical link between complexes and assembly rules

Provides diagrammatic tools for complex system analysis

Abstract

Large complexes of classical particles play central roles in biology, in polymer physics, and in other disciplines. However, physics currently lacks mathematical methods for describing such complexes in terms of component particles, interaction energies, and assembly rules. Here we describe a Fock space structure that addresses this need, as well as diagrammatic methods that facilitate the use of this formalism. These methods can dramatically simplify the equations governing both equilibrium and non-equilibrium stochastic chemical systems. A mathematical relationship between the set of all complexes and a list of rules for complex assembly is also identified.