Thermodynamic Characterization of Synchronization-Optimized Oscillator-Networks

TL;DR

This paper investigates the structure and thermodynamic properties of synchronization-optimized oscillator networks, revealing how network topology influences synchronization and exhibits anomalies in thermodynamic behavior.

Contribution

It introduces a novel MCMC approach using the Kirchhoff index to generate and analyze a large ensemble of optimized oscillator networks, linking topology to thermodynamic anomalies.

Findings

Transition from star to core-periphery structure depends on network connectivity.

Node degree variance characterizes the structural transition.

Sparse networks show anomalies in heat capacity.

Abstract

We consider a canonical ensemble of synchronization-optimized networks of identical oscillators under external noise. By performing a Markov chain Monte Carlo (MCMC) simulation using the Kirchhoff index, i.e., the sum of the inverse eigenvalues of the Laplacian matrix (as a graph Hamiltonian of the network), we construct more than 1,000 different synchronization-optimized networks. We then show that the transition from star to core-periphery structure depends on the connectivity of the network, and is characterized by the node degree variance of the synchronization-optimized ensemble. We find that thermodynamic properties such as heat capacity show anomalies for sparse networks.