We study a planar two-temperature diffusion of a Brownian particle in a parabolic potential. The diffusion process is defined in terms of two Langevin equations with two different effective temperatures in the $X$ and the $Y$ directions. In the stationary regime the system is described by a nontrivial particle position distribution, $P(x,y)$, which we determine explicitly. We show that this distribution corresponds to a nonequilibrium stationary state, characterized by the presence of space-dependent particle currents which exhibit a nonzero rotor. Theoretical results are confirmed by the numerical simulations.

• Received 20 March 2013

DOI:https://doi.org/10.1103/PhysRevE.87.062130