Adiabatic linear response and Einstein relation in non-equilibrium steady states for tilted periodic potentials
R. Salgado-García

Centre de Physique Theorique, UMR 7644 CNRS-Ecole Polytechnique, 91128 Palaiseau Cedex, France

Abstract: The adiabatic linear response for the steady state probability density function is calculated for tilted periodic potentials subject to an arbitrary probing force field. I show that for a suitable choice of the probing force field, the usual form of the Einstein relation holds in the non-equilibrium steady state regime. A violation function of the Einstein relation can be given analytically in terms of quadratures involving the probing force and the 'adjoint probability density'. The latter is given by the probability density function associated to the adjoint current operator of the non perturbed Fokker-Planck equation. All these findings are in good agreement with numerical Langevin simulations.