Quantum entanglement and Hawking temperature

TL;DR

This paper explores the relationship between quantum entanglement entropy and Hawking temperature in black holes, providing evidence that Hawking temperature relates to the rate of change of entanglement entropy, linking quantum information theory with black hole thermodynamics.

Contribution

It demonstrates, within the adiabatic approximation, that Hawking temperature can be derived from the rate of change of entanglement entropy across a black hole's horizon.

Findings

Hawking temperature relates to entanglement entropy change rate

No direct relation between entanglement entropy and temperature for black holes

Supports quantum information perspective on black hole thermodynamics

Abstract

The thermodynamic entropy of an isolated system is given by its von Neumann entropy. Over the last few years, there is an intense activity to understand thermodynamic entropy from the principles of quantum mechanics. More specifically, is there a relation between the (von Neumann) entropy of entanglement between a system and some (separate) environment is related to the thermodynamic entropy? It is difficult to obtain the relation for many body systems, hence, most of the work in the literature has focused on small number systems. In this work, we consider black-holes --- that are simple yet macroscopic systems --- and show that a direct connection could not be made between the entropy of entanglement and the Hawking temperature. In this work, within the adiabatic approximation, we explicitly show that the Hawking temperature is indeed given by the rate of change of the entropy of entanglement across a black hole's horizon with regard to the system energy. This is yet another numerical evidence to understand the key features of black hole thermodynamics from the viewpoint of quantum information theory.