Non-equilibrium mean-field theories on scale-free networks

TL;DR

This paper introduces a systematic method for deriving non-equilibrium mean-field theories on scale-free networks, accurately capturing critical behaviors influenced by degree heterogeneity in various models.

Contribution

It presents a novel approach to derive stochastic mean-field equations that incorporate degree heterogeneity, improving predictions of critical dynamics on scale-free networks.

Findings

Successfully predicts critical behavior of binary spin models

Accurately models reaction-diffusion processes

Links non-equilibrium theories with generalized Landau theory

Abstract

Many non-equilibrium processes on scale-free networks present anomalous critical behavior that is not explained by standard mean-field theories. We propose a systematic method to derive stochastic equations for mean-field order parameters that implicitly account for the degree heterogeneity. The method is used to correctly predict the dynamical critical behavior of some binary spin models and reaction-diffusion processes. The validity of our non-equilibrium theory is furtherly supported by showing its relation with the generalized Landau theory of equilibrium critical phenomena on networks.