Noise-Induced Phase Transition: Zero-Dimensional Brownian Particles Varying between Ergodicity and Nonergodicity

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We study in phase space a zero-dimensional system of Brownian particles which move in a periodic potential and subject to an internal time derivative Ornstein–Uhlenbeck noise. To resolve the Fokker–Planck equation in such a case, we propose an approximate analytical method. The theoretical predictions exhibit a second order noise-induced nonequilibrium phase transition, which is confirmed by numerical simulation results. The phase transition brings the system from an ergodicity to a nonergodicity phase as the potential barrier height decreases.