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