Energy dynamics, information and heat flow in quenched cooling and the crossover from quantum to classical thermodynamics

TL;DR

This paper explores the initial energy and entropy dynamics when two quantum many-body systems are suddenly brought into contact, revealing quantum-origin energy increases and the transition to classical thermodynamics.

Contribution

It uncovers the quantum energy increase linked to entropy gain at short times and demonstrates the crossover to classical energy dynamics in many-body quantum systems.

Findings

Initial energy increase occurs in both systems due to quantum correlations.

Quantum origin of energy increase is linked to collective binding energy.

Classical energy dynamics emerge when energy relaxation dominates.

Abstract

The dynamics when a hot many-body quantum system is brought into instantaneous contact with a cold many-body quantum system can be understood as a combination of early time quantum correlation (von Neumann entropy) gain and late time energy relaxation. We show that at the shortest timescales there is an energy increase in each system linked to the entropy gain, even though equilibrium thermodynamics does not apply. This energy increase is of quantum origin and results from the collective binding energy between the two systems. Counter-intuitively, this implies that also the hotter of the two systems generically experiences an initial energy increase when brought into contact with the other colder system. In the limit where the energy relaxation overwhelms the (quantum) correlation build-up, classical energy dynamics emerges where the energy in the hot system decreases immediately upon contact with a cooler system. We use both strongly correlated SYK systems and weakly correlated mixed field Ising chains to exhibit these characteristics, and comment on its implications for both black hole evaporation and quantum thermodynamics.