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Usually time of passage across a region may be expected to increase with thenumber of barriers along the path. Can this intuition fail depending on thespecial nature of the barrier? We study experimentally the transport of arobotic bug which navigates through a spatially patterned array of obstacles.Depending on the nature of the obstacles we call them either entropic orenergetic barriers. For energetic barriers we find that the timescales of firstpassage vary non-monotonically with the number of barriers, while for entropicbarriers first passage times increase monotonically. We perform an exactanalytic calculation to derive closed form solutions for the mean first passagetime for different theoretical models of diffusion. Our analytic resultscapture this counter-intuitive non-monotonic behaviour for energetic barriers.We also show non-monotonic effective diffusivity in the case of energeticbarriers. Finally, using numerical simulations, we show this non-monotonicbehaviour for energetic barriers continues to hold true for super-diffusivetransport. These results may be relevant for timescales of intra-cellularbiological processes.

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