  We investigate the stochastic behavior of a two-temperature Langevin system
with non-Markovian thermal reservoirs. The model describes an overdamped
Brownian particle in a quadratic potential and coupled to heat baths at
different temperatures. The reservoirs are characterized by Gaussian white and
colored noises and a dissipation memory kernel. The stationary states present
non-trivial average rotational motion influenced by stochastic torques due to
harmonic, friction and fluctuating thermal forces. However, the Markovian limit
leads to a vanishing average torque produced by fluctuating thermal forces. We
also study the effects of memory on the stochastic heat and the entropy
production in the steady-state regime.
