  Intuition suggests that passage times across a region increases with the
number of barriers along the path. Can this fail depending on the nature of the
barrier? To probe this fundamental question, we exactly solve for the first
passage time in general d-dimensions for diffusive transport through a
spatially patterned array of obstacles - either entropic or energetic,
depending on the nature of the obstacles. For energetic barriers, we show that
first passage times vary non-monotonically with the number of barriers, while
for entropic barriers it increases monotonically. This non-monotonicity for
energetic barriers further reflects in the behaviour of effective diffusivity
as well. We then design a simple experiment where a robotic bug navigates a
heterogeneous environment through a spatially patterned array of obstacles to
validate our predictions. Finally, using numerical simulations, we show that
this non-monotonic behaviour for energetic barriers is general and extends to
even super-diffusive transport.
