The Brownian motion in a thermal field

The diffusion of a Brownian particle in a continuum subject to external potential forces as well as nonhomogeneous thermal field is discussed. Apart from a thermodiffusion phenomenon, a Streater effect in which the potential energy of the particle is converted to a heat due to friction cf. R.F. Streater, Rep. Math. Phys. 40, 557 (1997), is taken into account. It is shown that for such a continuum the first law of thermodynamics holds true, and the second law is observed if a relation between the probability density function and temperature is satisfied. The examples of the Brownian motion for particular external fields are given.