Entanglement Thermodynamics

TL;DR

The work investigates entanglement entropy for excited states using holographic entanglement entropy, deriving a first-law–like relation that connects changes in entanglement entropy, energy, and entanglement pressure for small subsystems via a region-size–dependent entanglement temperature. It demonstrates universal features for spherical entangling regions, showing a simple energy–entropy relation with a universal temperature scaling, and discusses the role of entanglement pressure. Building on this, the authors propose four laws of entanglement thermodynamics, including zeroth-, first-, second-, and third-law–type statements, while acknowledging limits of generality and extensions to time-dependent or covariant contexts. The paper suggests a structured framework to understand entanglement in non-equilibrium settings and its holographic description, pointing toward broader implications for quantum information in strongly coupled systems.

Abstract

We study entanglement entropy for an excited state by making use of the proposed holographic description of the entanglement entropy. For a sufficiently small entangling region and with reasonable identifications we find an equation between entanglement entropy and energy which is reminiscent of the first law of thermodynamics. We then suggest four statements which might be thought of as four laws of entanglement thermodynamics.