Theory of Hot Brownian Motion

The erratic motion of suspended colloidal particles due to thermal fluctuations of the solvent molecules is well known as Brownian motion and has long found its theoretical explanation as an equilibrium phenomenon. In this work, we abandon the homogeneity of temperature and viscosity and address so-called hot Brownian motion [Rings et al., Phys. Rev. Lett., 2010, 105 (9), 090604] of (laser-)heated nanoparticles. We develop an effective Markovian equilibrium description for this non-equilibrium phenomenon by deriving the appropriate effective temperature and viscosity parameters from a generalized theory of fluctuating hydrodynamics. On the basis of our systematic mathematical formulation we propose a numerically accurate simplified model that yields analytical results.