Sensitivity analysis of cycle flux response in nonequilibrium dynamics

The decomposition of edge current into cycle fluxes sheds light on understanding the nonequilibrium steady state structure of stochastic graph models, providing important insights into irreversibility, stability, and dominant functionality of a plethora of nonequilibrium physics. However, the response of the cycle flux to time-dependent perturbations is less well understood. Here, we introduce a theoretical method to analyze the response properties of the cycle flux around the nonequilibrium steady state, rather than the near equilibrium response provided by the well-known linear response theory. We find that both the state and cycle flux responses are determined by the system relaxation spectrum, the signal frequency, as well as the overlap between the signal matrix and the transient states. We further study the relation between response sensitivity and the information gain contained in the stochastic trajectory, providing an information theoretic bound on cycle flux response precision. Furthermore, we use both a quantum Maxwell demon model and a classical chemical reaction network model to illustrate our theory. Our work paves the way toward fully understanding and controlling the dynamical response of complex nonequilibrium stochastic graph models and inferring the hidden time-dependent signals by measuring the observable cycle flux response.