Geometrical Derivation of Equilibrium Distributions in some Stochastic Systems

TL;DR

This paper introduces a geometric approach to derive equilibrium distributions in stochastic systems, emphasizing the equivalence of different statistical methods in multi-agent contexts.

Contribution

It provides a novel geometric derivation of equilibrium distributions and demonstrates their equivalence in multi-agent systems, extending thermodynamic concepts.

Findings

Geometric derivation of equilibrium distributions

Equivalence of volume-based and surface-based calculations

Application to multi-agent systems

Abstract

In this chapter, we present a straightforward geometrical argument that in a certain way recalls us the equivalence between the canonical and the microcanonical ensembles in the thermodynamic limit for the particular context of physical sciences. In the more general context of homogeneous multi-agent systems, we conclude by highlighting the statistical equivalence of the volume-based and surface-based calculations in this type of systems.