Equilibrium distributions in entropy driven balanced processes

TL;DR

This paper explores how entropy-driven processes lead to specific equilibrium distributions like Poisson and negative binomial, with applications in complex networks and particle physics, revealing the underlying statistical mechanics of these systems.

Contribution

It derives the equilibrium distributions for entropy-driven balanced processes and applies them to network degree distributions and particle systems.

Findings

Final states include Poisson, Bernoulli, negative binomial, and Pólya distributions.

Application to network degree evolution shows specific distribution patterns.

Application to particle systems demonstrates distribution of particles among states.

Abstract

For entropy driven balanced processes we obtain final states with Poisson, Bernoulli, negative binomial and P\'olya distributions. We apply this both for complex networks and particle production. For random networks we follow the evolution of the degree distribution, $P_n$, in a system where a node can activate $k$ fixed connections from $K$ possible partnerships among all nodes. The total number of connections, $N$, is also fixed. For particle physics problems $P_n$ is the probability of having $n$ particles (or other quanta) distributed among $k$ states (phase space cells) while altogether a fixed number of $N$ particles reside on $K$ states.