  We show that when Brownian motion takes place in a heterogeneous medium, the
presence of local forces and transport coefficients leads to deviations from a
Gaussian probability distribution that make that the ratio between forward and
backward probabilities depends on the nature of the host medium, on local
forces and also on time. We have applied our results to two situations:
diffusion in a disordered medium and diffusion in a confined system. For such
scenarios we have shown that our theoretical predictions are in very good
agreement with numerical results. Moreover we have shown that the deviations
from the Gaussian solution lead to the onset of rectification. Our predictions
could be used to detect the presence of local forces and to characterize the
intrinsic short-scale properties of the host medium, a problem of current
interest in the study of micro and nano-systems.
