  We investigate a system composed of two coupled oscillators subject to
stochastic fluctuations in its internal parameters. In particular, we answer
the question whether the well-known classical analogy of the quantum dynamics
of two-level systems (TLS), i.e. qubits, provided by two coupled oscillators
can be extended to simulate the dynamics of dissipative quantum systems. In the
context of nanomechanics, the analogy in the dissipation free case has already
been tested in multiple experimental setups, e.g., doubly clamped or cantilever
string resonators and optically levitated particles. A well-known result of
this classical analogy is that the relaxation and decoherence times of the
analog quantum system must be equal, i.e. $T_1=T_2$, in contrast to the general
case of quantum TLS. We show that this fundamentally quantum feature, i.e.
$T_1\neq T_2$, can be implemented as well in the aforementioned classical
systems by adding stochastic fluctuations in their internal parameters.
Moreover, we show that these stochastic contributions can be engineered in the
control apparatus of those systems, discussing, in particular, the application
of this theory to levitated nanoparticles and to nanostring resonators.
