Drift-diffusion processes from elimination of fast variables under inhomogeneous conditions

Abstract

The problem of eliminating fast-relaxing variables to obtain an effective drift-diffusion process in position is solved in a uniform and straightforward way for models with velocity a function jointly of position and fast variables. A more unified view is thereby obtained of the effect of environmental inhomgeneity on the motion of a diffusing particle, in particular, whether a drift is induced, covering both passive and active particles. Infinitesimal generators (equivalently, drift-diffusion fields) for the contracted processes are worked out in detail for several models.

10 pages. Abstract, introduction, and conclusion have been rewritten to improve clarity

References in corpus (3)

• When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation
• Derivation of a Langevin equation in a system with multiple scales: the case of negative temperatures
• Distinguishing Advective and Powered Motion in Self-Propelled Colloids