Entropic pulling and diffusion diode in an It\^o process

Biological environments at micrometer scales and below are often crowded, and experience incessant stochastic thermal fluctuations. The presence of membranes/pores, and multiple biological entities in a constricted space can make the damping/diffusion inhomogeneous. This effect of inhomogeneity is presented by the diffusion becoming coordinate-dependent. In this paper, we analyze the consequence of inhomogeneity-induced coordinate-dependent diffusion on Brownian systems in thermal equilibrium under the It\^o's interpretation. We argue that the presence of coordinate-dependent diffusion under It\^o's formulation gives rise to an effective diffusion potential (and, equivalently an entropy) that can have substantial contribution to system's transport. This emergent force when looked at as of entropic origin it provides a physical basis of the notion of the entropic pulling postulated in the context of working of some biological systems.