Universal Constraints on Energy Flow and SYK Thermalization

TL;DR

This paper establishes universal energy flow bounds in quantum systems coupled to baths, with applications to holography and SYK models, providing insights into black hole evaporation and energy conditions.

Contribution

It introduces a universal positivity bound on energy change rates and applies it to holographic and SYK systems, linking quantum dynamics to gravitational phenomena.

Findings

Derived a universal bound on energy flow in quantum systems.

Applied the bound to holographic models, connecting to energy conditions.

Analyzed SYK model dynamics and black hole evaporation in JT gravity.

Abstract

We study the dynamics of a quantum system in thermal equilibrium that is suddenly coupled to a bath at a different temperature, a situation inspired by a particular black hole evaporation protocol. We prove a universal positivity bound on the integrated rate of change of the system energy which holds perturbatively in the system-bath coupling. Applied to holographic systems, this bound implies a particular instance of the averaged null energy condition. We also study in detail the particular case of two coupled SYK models in the limit of many fermions using the Schwinger-Keldysh non-equilibrium formalism. We solve the resulting Kadanoff-Baym equations both numerically and analytically in various limits. In particular, by going to low temperature, this setup enables a detailed study of the evaporation of black holes in JT gravity.