Energetic and entropic vibrational resonance

The influence of an energetic bistable potential on the entropic vibrational resonance (EVR) is investigated. We demonstrate the existence of vibrational resonance modulated by the high-frequency signal with energetic and entropic barriers, which is termed energetic and entropic vibrational resonance (EEVR). We use different methods, including the numerical simulation of Langevin equation, the numerical solution of Fokker-Planck equation, and the analytical expressions of two-state approximation theory, to obtain the spectral amplification factor which can be used to quantify EEVR. In addition, there are two mechanisms, the dynamical phase transition of the stable states and the matching between the escape rate and low-frequency signal on time-scale in the EEVR, which are caused by the modulation of the high-frequency signal. Finally, an auxiliary quantity called the mean entropic Poisson intensity is proposed to describe the constraint effects of the uneven boundaries on the Brownian motion. The above research provides some theoretical reference for the detection of weak signals, and the manipulation of motions of an overdamped Brownian particles, under uneven boundary constraints in small-scale stochastic systems.