## Department of Physics Papers

#### Document Type

Journal Article

#### Date of this Version

7-27-2007

#### Abstract

The friction coefficient of a particle can depend on its position, as it does when the particle is near a wall. We formulate the dynamics of particles with such state-dependent friction coefficients in terms of a general Langevin equation with multiplicative noise, whose evaluation requires the introduction of specific rules. Two common conventions, the Ito and the Stratonovich, provide alternative rules for evaluation of the noise, but other conventions are possible. We show that the requirement that a particle’s distribution function approach the Boltzmann distribution at long times dictates that a drift term must be added to the Langevin equation. This drift term is proportional to the derivative of the diffusion coefficient times a factor that depends on the convention used to define the multiplicative noise. We explore the consequences of this result in a number of examples with spatially varying diffusion coefficients. We also derive a path integral representation for arbitrary interpretation of the noise, and use it in a perturbative study of correlations in a simple system.

#### Recommended Citation

Lau, A. W., & Lubensky, T. C. (2007). State-Dependent Diffusion: Thermodynamic Consistency and its Path Integral Formulation. Retrieved from https://repository.upenn.edu/physics_papers/155

**Date Posted:** 18 May 2011

This document has been peer reviewed.

## Comments

Suggested Citation:

A.W.C. Lau and T.C. Lubensky. (2007). State-dependent diffusion: Thermodynamic consistency and its path integral formulation.

Physical Review E,76, 011123.© 2007 The American Physical Society

http://dx.doi.org/10.1103/PhysReve.76.011123