  The foundations of statistical mechanics, namely how equilibrium hypothesis
emerges microscopically from quantum theory, is explored through investigating
the environment-induced quantum decoherence processes. Based on the recent
results on non-Markovian dynamics [Phys. Rev. Lett. 109, 170402 (2012)], we
find that decoherence of quantum states manifests unexpected complexities.
Indeed, an arbitrary given initial quantum state, under the influence of
different reservoirs, can evolve into four different steady states: thermal,
thermal-like, quantum memory and oscillating quantum memory states. The first
two steady states \textit{de facto} provided a rigorous proof how the system
relaxes to thermal equilibrium with its environment. The latter two steady
states, with strong non-Markovian effects, will maintain the initial state
information and not reach thermal equilibrium, which is beyond the conventional
wisdom of statistical mechanics.
