Peaceful coexistence of thermal equilibrium and the emergence of time

We consider a quantum universe composed of small system $S$ and large environment. It has been demonstrated that, for the vast majority randomly chosen wave functions satisfying total energy constraint, reduced density matrix is given by canonical statistical distribution. Here, through Page-Wootters mechanism, we show that time nonequilibrium dynamics can emerge as consequence entanglement between environment present in (randomly chosen) global function universe. The clock provided environment, which ticks temporal evolution $S$. paradox peaceful coexistence equilibrium solved identifying trace over degrees freedom with entire history