  We study the dynamics of a macroscopic superconducting qubit coupled to two
independent non-stationary reservoirs by using time-dependent perturbation
theory. We show that an equilibrium environment surpasses the coherent
evolution of the macroscopic qubit completely. When the qubit couples to two
different reservoirs, exemplifying a non-equilibrium environment, the
short-time dynamics is affected by the interference between two reservoirs,
implying the non-additivity of effects of two reservoirs. The non-additivity
can be traced back to a non-Markovian effect, even though two reservoirs are
independently assumed to be Markovian. Explicitly, the non-equilibrium
environment intensifies both coherent and incoherent parts of the evolution.
Therefore, the macroscopic qubit would evolve more coherently but at the price
of a shorter decoherence time.
