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

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.