Effective temperatures of a heated Brownian particle

We investigate various possible definitions of an effective temperature for a particularly simple nonequilibrium stationary system, namely a heated Brownian particle suspended in a fluid. The effective temperature based on the fluctuation dissipation ratio depends on the time scale under consideration, so that a simple Langevin description of the heated particle is not possible on short time scales. The short- and long-time limits of this effective temperature are shown to be consistent with the temperatures estimated from the kinetic energy and Einstein relation, respectively. The transient fluctuation theorem provides still another definition of the temperature, which is shown to coincide with the short-time value of the fluctuation dissipation ratio.