Dynamic hysteresis and transitions controlled by asymmetry in potential: energetic and entropic aspects

Abstract

We aim to investigate the precise role of the asymmetry in the underlying potential on the process of dynamic hysteresis. So far, the theoretical modeling of this phenomenon of fundamental importance has been done considering symmetric bistable systems. The influence of asymmetry in the bistable potential has been explored in related contexts, such as first passage time estimates, escape dynamics, stochastic resonance, etc., highlighting the importance of the aspect of asymmetry in the systems. However, the perspective of developing a thorough theoretical understanding in this context remained overlooked in the case of dynamic hysteresis. Here, we scrutinize how the asymmetry in the potential influences this process, considering the physical model of a Brownian particle in a double-well potential subject to a periodic forcing. We analyze in detail the effect of two distinct types of asymmetry in the intrinsic potential, one corresponding to the different depths and the other subject to the separate widths of the two wells of the double-well potential representing the bistable system. Our study reveals that the hysteretic effect predominantly decreases with increasing asymmetry in both types of the system, reflected in the reduced hysteresis loop area. This observation suggests that the introduction of the appropriate asymmetry in the potential can quantitatively regulate the outputs of the dynamic hysteresis. This modulation can be beneficial for controlling devices' outputs in which dynamic hysteresis plays a role. Moreover, importantly, the implemented asymmetries in the potential can induce symmetry breaking in the response of the systems. This gives rise to asymmetric dynamic hysteresis loops, signifying the dynamic transition to an asymmetric phase, in moderate conditions, which is absent in the symmetric systems in the same scenarios.