Linear response in noisy network dynamics due to parameter changes

Rong-Chih Chang^1*

¹Physics, National Central University, Taoyuan, Taiwan

* Presenter:Rong-Chih Chang, email:zxc22762246@gmail.com

It is known that linear response theory (LRT) is a framework for predicting a system’s response to small perturbations, linking the response to equilibrium correlation functions. In this work, we develop and extend linear response theory (LRT) to noisy directed network dynamics under parameter changes. We analyze networks where each node experiences noise and fluctuates around steady states, systematically perturbing parameters like connection weights. We derive steady-state and time-dependent response functions, interpreting system responses as transitions between nonequilibrium steady states (NESS). The framework generalizes LRT to nonequilibrium networks by linking responses to correlation functions from the unperturbed state, revealing the impact of asymmetric directed connections and noise heterogeneity on breaking time-reversal symmetry. Through analytical derivations and Langevin simulations, the study quantifies network responses, identifies critical nodes, and connects these results to thermodynamic quantities, including entropy production, heat, and work rates. The work provides predictive tools to evaluate disruptions in complex networks ranging from biological to engineered systems, deepening understanding of nonequilibrium stochastic dynamics and resilience in directed noisy networks.

Keywords: Linear response theory, Fluctuation-dissipation theorem, Complex network