Emergent complexity in slowly driven stochastic processes.

We consider the distribution of first passage time events in the presence of non-ergodic modes that drive otherwise ergodic dynamics on a potential landscape. We find that in the limit of slow and large enough fluctuations the distribution of first passage time events, f ( t ), exhibits heavy tails dominated by a power law with exponent f ( t ) ~ t âˆ'2 , and corrections that depend on the strength and the nature of fluctuations. We support our theoretical findings through direct numerical simulations in illustrative examples.