  As an application of the classically decayable correlation in a quantum chaos
system maintained over an extremely long time-scale (Matsui et al,
Europhys.Lett. 113(2016),40008), we propose a minimal model of quantum damper
composed of a quantum harmonic oscillator (HO) weakly interacting with a
bounded quantum chaos system. Although the whole system obeys unitary evolution
dynamics of only three quantum degrees of freedom, the mechanical work applied
to the HO is stationary converted into the "internal energy" characterized by
an effective temperature in an irreversible way over a sufficiently long
time-scale, if the components of the quantum chaos system are mutually
entangled enough. A paradoxical dependence of the duration time of the
stationary conversion on the driving strength is also discussed.
