Hot Brownian motion

Hot Brownian motion is the diffusive motion of a colloidal particle which is maintained at higher temperature than its solvent, e.g. by laser light absorption. After a brief review of the stochastic theory of diffusion, I will present its extension, based on fluctuating hydrodynamics, to the case of hot Brownian motion. In particular I will show that the random dynamics of the hot particle is governed by a frequency dependent effective temperature which results from the coupling of the hydrodynamic modes with the temperature inhomogeneities in the fluid. Conceptually, this lays the basis for out-of equilibrium statistical mechanics of Brownian motion under general non-isothermal conditions.