Peaceful coexistence of thermal equilibrium and the emergence of time

TL;DR

This paper demonstrates how time and non-equilibrium dynamics can emerge from a quantum universe in thermal equilibrium through entanglement, using the Page and Wootters mechanism, reconciling statistical equilibrium with dynamic evolution.

Contribution

It introduces a framework where time and dynamics emerge from entanglement in a quantum universe, resolving the paradox of coexistence of equilibrium and non-equilibrium states.

Findings

Time and dynamics emerge from entanglement in a quantum universe.

The environment acts as a clock for the system's evolution.

Statistical equilibrium coexists with non-equilibrium dynamics through entanglement.

Abstract

We consider a quantum Universe composed by 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 and Wootters mechanism, we show that time and non-equilibrium 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 non-equilibrium 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.