Can the entanglement entropy be the origin of black-hole entropy ?

TL;DR

This paper investigates whether entanglement entropy can be the origin of black-hole entropy by constructing a thermodynamics of entanglement and comparing it with black-hole thermodynamics, considering gravitational effects.

Contribution

It introduces a framework for entanglement thermodynamics with different definitions of entanglement energy and analyzes the impact of gravity on this thermodynamics.

Findings

Entanglement thermodynamics differs from black-hole thermodynamics without gravity.

Including gravity makes entanglement thermodynamics resemble black-hole thermodynamics.

Entanglement entropy passes a non-trivial check as a candidate for black-hole entropy.

Abstract

Entanglement entropy is often speculated as a strong candidate for the origin of the black-hole entropy. To judge whether this speculation is true or not, it is effective to investigate the whole structure of thermodynamics obtained from the entanglement entropy, rather than just to examine the apparent structure of the entropy alone or to compare it with that of the black hole entropy. It is because entropy acquires a physical significance only when it is related to the energy and the temperature of a system. From this point of view, we construct a `thermodynamics of entanglement' by introducing an entanglement energy and compare it with the black-hole thermodynamics. We consider two possible definitions of entanglement energy. Then we construct two different kinds of thermodynamics by combining each of these different definitions of entanglement energy with the entanglement entropy. We find that both of these two kinds of thermodynamics show significant differences from the black-hole thermodynamics if no gravitational effects are taken into account. These differences are in particular highlighted in the context of the third law of thermodynamics. Finally we see how inclusion of gravity alter the thermodynamics of the entanglement. We give a suggestive argument that the thermodynamics of the entanglement behaves like the black-hole thermodynamics if the gravitational effects are included properly. Thus the entanglement entropy passes a non-trivial check to be the origin of the black-hole entropy.