  We consider the effects of memory on the stationary behavior of a
two-dimensional Langevin dynamics in a confining potential. The system is
treated in an overdamped approximation and the degrees of freedom are under the
influence of distinct kinds of stochastic forces, described by Gaussian white
and colored noises, as well as different effective temperatures. The joint
distribution function is calculated by time-averaging approaches, and the
long-term behavior is analyzed. We determine the influence of noise temporal
correlations on the steady-state behavior of heat flux and entropy production.
Non-Markovian effects lead to a decaying heat exchange with spring force
parameter, which is in contrast to the usual linear dependence when only
Gaussian white noises are presented in overdamped treatments. Also, the model
exhibits non-equilibrium states characterized by a decreasing entropy
production with memory time-scale.
