Stochastic Resonance for Non-Equilibrium Systems

Abstract: Stochastic resonance (SR) is a prominent phenomenon in many natural and engineered noisy system, whereby the response to a periodic forcing is greatly amplified when the intensity of the noise is tuned to within a specific range of values. We propose here a general mathematical framework based on large deviation theory, and, specifically, on the theory of quasi-potentials, for describing SR in noisy N-dimensional non-equilibrium systems possessing two metastable states and undergoing a periodically modulated forcing. The drift and the volatility fields of the equations of motion can be fairly general and the competing attractors of the deterministic dynamics and the edge state living on the basin boundary can, in principle, feature chaotic dynamics. Similarly, the perturbation field of the forcing can be fairly general. Our approach is able to recover as special cases the classical results previously presented in the literature for systems obeying detailed balance and allows for expressing the parameters describing SR and the statistics of residence times in the two-state approximation in terms of the unperturbed drift field, the volatility field, and the perturbation field. We clarify which specific properties of the forcing are relevant for amplifying or suppressing SR in a system, and classify forcings according to classes of equivalence. Our results indicate a route for a detailed understanding of SR in rather general systems.