Entropic pulling and diffusion diode in an Itô process

Abstract

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 Itô's interpretation. We argue that the presence of coordinate-dependent diffusion under Itô'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.

9 pages, 7 figures. Diffusivity has been set to order of unity in sections II and III, unless stated otherwise. A new paragraph has also been added towards the end of section III