  Time-irreversibility is a distinctive feature of non-equilibrium dynamics and
several measures of irreversibility have been introduced to assess the distance
from thermal equilibrium of a stochastically driven system. While the dynamical
noise is often approximated as white, in many real applications the time
correlations of the random forces can actually be significantly long-lived
compared to the relaxation times of the driven system. We analyze the effects
of temporal correlations in the noise on commonly used measures of
irreversibility and demonstrate how the theoretical framework for white noise
driven systems naturally generalizes to the case of colored noise.
Specifically, we express the auto-correlation function, the area enclosing
rates, and mean phase space velocity in terms of solutions of a Lyapunov
equation and in terms of their white noise limit values.
