Equilibrium of a Brownian particle in a damping induced inhomogeneous space: an alternative approach

Abstract

We look at the equilibrium of a Brownian particle in an inhomogeneous space following the alternative approach proposed in (Bhattacharyay 2013 Physica A 392 4265). We consider a coordinate dependent damping resulting in a stochastic problem with multiplicative noise. We convert this stochastic problem with multiplicative noise to additive noise form using our alternative approach. The resulting equilibrium velocity distribution is locally Maxwellian with a zero mean. The position distribution is of a modified Boltzmann form where that of a free particle is a function of damping constant.