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.

研究了高能双稳态势对熵振动共振 (EVR) 的影响。我们证明了由具有能量和熵势垒的高频信号调制的振动共振的存在，这被称为能量和熵振动共振 (EEVR)。我们使用不同的方法，包括朗之万方程的数值模拟、Fokker-Planck 方程的数值解以及二态逼近理论的解析表达式，以获得可用于量化EEVR 的频谱放大因子。此外，EEVR中还有两种机制，即稳态的动态相变以及逃逸率与低频信号在时间尺度上的匹配，这是由高频信号的调制引起的。最后，提出了一个称为平均熵泊松强度的辅助量来描述不均匀边界对布朗运动的约束作用。上述研究为小尺度随机系统中不均匀边界约束下弱信号的检测和过阻尼布朗粒子的运动控制提供了一定的理论参考。