Effective Diffusion and transport coherence in presence of inhomogeneous temeprature: Piecewise linear potential

TL;DR

This paper derives analytical formulas for the diffusion coefficient of a Brownian particle in a piecewise linear potential with spatially varying temperature, enhancing understanding of transport coherence in inhomogeneous thermal environments.

Contribution

It provides explicit analytical expressions for current and diffusion coefficients in a complex inhomogeneous temperature setting, advancing theoretical modeling of Brownian motors.

Findings

Analytical formulas match numerical simulations.

Inhomogeneous temperature significantly affects diffusion.

Transport coherence can be optimized by potential design.

Abstract

We compute the effective diffusion coefficient of a Brownian particle in a piece-wise linear periodic potential and subject of spatially inhomogeneous temperature, otherwise known as the B{\"u}ttiker-Landauer motor. We obtain analytical expressions for the current and diffusion coefficients and compare with numerical results.