Entropic pulling and diffusion diode in an Itô process

Abstract

Biological environments at micrometre 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 letter, we analyse the consequence of inhomogeneity-induced coordinate-dependent diffusion on Brownian systems in thermal equilibrium under Itô's interpretation. The Itô-distribution comprises the Boltzmann factor (canonical part) and a factor of inverse diffusivity, when diffusion is coordinate-dependent, which is the microcanonical density of state. The Itô-distribution and the process is thus completely consistent with the Boltzmann-Gibbs measure. The density of state results in an emergent force of entropic origin, which can have substantial effects on diffusive transport processes. The present letter demonstrates these novel transport processes by computer simulations of many-body systems in the overdamped limit.