Hot brownian motion.

We derive the markovian description for the nonequilibrium brownian motion of a heated nanoparticle in a simple solvent with a temperature-dependent viscosity. Our analytical results for the generalized fluctuation-dissipation and Stokes-Einstein relations compare favorably with measurements of laser-heated gold nanoparticles and provide a practical rational basis for emerging photothermal tracer and nanoparticle trapping and tracking techniques.