  We provide a simple hypocoercivity analysis for the effective Mori-Zwanzig
equation governing the time evolution of noise-averaged observables in a
stochastic dynamical system. Under the hypocoercivity framework mainly
developed by Dolbeault, Mouhot and Schmeiser and further extended by Grothaus
and Stilgenbauer, we prove that under the same conditions which lead to the
geometric ergodicity of the Markov semigroup $e^{tK}$, the Mori-Zwanzig
orthogonal semigroup $e^{tQKQ}$ is also geometrically ergodic, provided that
$P=I-Q$ is a finite-rank, orthogonal projection operator in a certain Hilbert
space. The result is applied to the widely used Mori-type effective
Mori-Zwanzig equations in the coarse-grained modeling of molecular dynamics and
leads to exponentially decaying estimates for the memory kernel and the
fluctuation force.
