Equilibrium with coordinate dependent diffusion: Comparison of different stochastic processes

2023/09/10 by Bhattacharyay, A.
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2309.06567

Abstract

We show that, simultaneous local scaling of coordinate and time keeping the velocity unaltered is a symmetry of an Itô-process. Using this symmetry, any Itô-process can be mapped to a universal additive Gaussian-noise form. We use this mapping to separate the canonical and micro-canonical part of stochastic dynamics of a Brownian particle undergoing coordinate dependent diffusion. We identify the equilibrium distribution of the system and associated entropy induced by coordinate dependence of diffusion. Equilibrium physics of such a Brownian particle in a heat-bath of constant temperature is that of an Itô-process.

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