Rewiring driven evolution of quenched frustrated signed network

TL;DR

This paper develops a theoretical framework to analyze the evolution of frustrated signed networks under random rewiring, deriving stationary distributions and exact solutions through master equations and stochastic process mappings.

Contribution

It introduces a novel approach combining master equations and birth-death process mappings to analyze network frustration dynamics.

Findings

Derived stationary thermodynamic distribution for the network.

Provided exact solutions via stochastic process mapping.

Validated theoretical estimates with numerical simulations.

Abstract

A framework for studying the behavior of a classically frustrated signed network in the process of random rewiring is developed. We describe jump probabilities for change in frustration and formulate a theoretical estimate in terms of the master equation. Stationary thermodynamic distribution and moments are derived from the master equation and compared to numerical simulations. Furthermore, an exact solution of the probability distribution is provided through suitable mapping of rewiring dynamic to birth and death processes with quadratic asymptotically symmetric transition rates.