The effective diffusion coefficient for the overdamped Brownian motion in a tilted periodic potential is calculated in closed analytical form. Universality classes and scaling properties for weak thermal noise are identified near the threshold tilt where deterministic running solutions set in. In this regime the diffusion may be greatly enhanced, as compared to free thermal diffusion with, for a realistic experimental setup, an enhancement of up to 14 orders of magnitude.

An exact analytical expression for the effective diffusion coefficient of an overdamped Brownian particle in a tilted periodic potential is derived for arbitrary potentials and arbitrary strengths of the thermal noise. Near the critical tilt ͑threshold of deterministic running solutions͒ a scaling behavior for weak thermal noise is revealed and various universality classes are identified. In comparison with the bare ͑potential-free͒ thermal diffusion, the effective diffusion coefficient in a critically tilted periodic potential may be, in principle, arbitrarily enhanced. For a realistic experimental setup, an enhancement by 14 orders of magnitude is predicted so that thermal diffusion should be observable on a macroscopic scale at room temperature.

No abstract

By considering an ensemble of Brownian particles suspended in a heat bath as a thermodynamic system with an internal degree of freedom it is possible to obtain the Fokker-Planck equation for Brownian motion in a temperature gradient, by applying the scheme of non-equilibrium thermodynamics. We recover explicitely the equations derived in particular by Zubarev and Bashkirov using statistical mechanical and kinetic methods. In addition when the temperature gradient does not have an externally imposed magnitude we obtain the differential equation for the temperature field, which is coupled to the Fokker-Planck equation.

A thermodynamics for systems at a stationary state is formulated. It is based upon the assumption of the existence of local equilibrium in phase space which enables one to interpret the probability density and its conjugated nonequilibrium chemical potential as mesoscopic thermodynamic variables. The probability current is obtained from the entropy production related to the probability diffusion process and leads to the formulation of the Fokker-Planck equation. For the case of a gas of Brownian particles under steady flow in the dilute and concentrated regimes we derive nonequilibrium equations of state.