Transport in Inhomogeneous Systems

In this paper, transport is considered in an infinite one-dimensional system where inhomogeneity is present. The formulation of transport is investigated for the most general case using the microscopic global reversibility (GR) symmetry and the generalized master equation corresponding to the separable continuous time random walk model. Familiar diffusion equations (classical and fractional (nonlocal and/or non-Markovian)) are revisited when applying special conditions on these general formulae.