Ergodic–Nonergodic Transition Induced by Non-Gaussian Noise

The ergodic behavior of a system subjected to both internal thermal and external non thermal noises has been studied, by using the Khinchin theorem. For the internal noise we have considered Gaussian white noise but the external noise non-Gaussian in characteristic. We discuss the process which is either free, or takes place in a bounded potential landscape. In a force-free case, the system is ergodic for q ≤ 1, whereas for q > 1 the ergodicity is breakdown. An ergodic–nonergodic transition is found at a critical value q = 1. After adding an external bounded potential, the ergodicity for q > 1 is recovered, which is the characteristic behavior of nonergodic Brownian motion of class-I. Furthermore, we compare our results with the ergodicity definition and Lee’s condition to discuss applicability of the latter within non-Gaussian Brownian dynamics.