Non-monotonic behavior of timescales of passage in heterogenous media : Dependence on the nature of barriers

Usually time of passage across a region maybe expected to increase with the number of barriers along the path. Can this intuition fail depending on the special nature of the barrier? We study experimentally the transport of a robotic bug which navigates through a spatially patterned array of obstacles. Depending on the nature of the obstacles we call them either entropic or energetic barriers. For the energetic barriers we find that the timescales of first passage vary non-monotonically with thenumber of barriers, while for entropic barriers first passage times increase monotonically. To explain this counter-intuitive phenomenon, we present analytically exact as well as simulation results of first passage times for different theoretical models of diffusion. We also show non-monotonic effective diffusivity in the case of energetic barriers. These results maybe relevant for timescales certain biological processes.