  We investigate the correspondence between classical noise and quantum
environments. Although it has been known that the classical noise can be mapped
to the quantum environments only for pure dephasing and infinite-temperature
dissipation processes, we describe that this limitation can be circumvented by
introducing auxiliary systems and conservation. Taking a two-level system as an
example, we construct the so-called central spin model with its couplings
fluctuating as the classical noise, and then acquire its statistical-average
dynamics which captures the dissipations beyond the infinite temperature. By
adjusting the number of the auxiliary systems and their initial states, the
noise-based model reproduces both Markovian and non-Markovian evolutions. It is
also found that different quantities of the two-level system are governed by
different model parameters, indicating that the constructed model is an
efficient simulator for specific observables, rather than an equivalent form of
a realistic open system. In addition, the model is also applicable to
investigate topical mechanisms of the open systems, e.g. negative temperatures
and asymmetric equidistant quenches.
