Stationary properties of a non-Markovian Brownian gyrator

We investigate the stochastic behavior of a non-Markovian version of an elementary Brownian gyrator. The model is defined by overdamped Langevin-like dynamics with a two-dimensional harmonic potential that presents distinct principal axes and is coupled to heat baths at different temperatures. The thermal noises are assumed to be Gaussian, and are related to friction forces through a dissipation memory kernel. The stationary states present rotational motion with non-trivial average torques due to harmonic, friction and fluctuating thermal forces. However, the Markovian limit of the system exhibits a zero average torque produced by fluctuating thermal forces. For the case of stochastic torque exerted by harmonic force, the cumulant-generating function is calculated exactly. We also study the average heat fluxes in the steady-state regime, where a memory-dependent behavior is observed.