BROWNIAN-MOTION IN THE PRESENCE OF A TEMPERATURE-GRADIENT

By considering an ensemble of Brownian particles suspended in a heat b ath 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 ther modynamics. We recover explicitely the equations derived in particular by Zubarev and Bashkirov using statistical mechanical and kinetic met hods. In addition when the temperature gradient does not have an exter nally imposed magnitude we obtain the differential equation for the te mperature field, which is coupled to the Fokker-Planck equation.