Thermodynamic law from the entanglement entropy bound

TL;DR

This paper explores how the saturation of the entanglement entropy bound leads to a thermodynamics-like law in quantum systems, revealing a universal relation for entanglement temperature and introducing the entanglement chemical potential.

Contribution

It demonstrates that the entanglement entropy bound's saturation results in a universal thermodynamics-like law and introduces the concept of entanglement chemical potential under global quenches.

Findings

Entanglement temperature is proportional to the inverse of system size.

Saturation of the entanglement entropy bound leads to a thermodynamics-like law.

Deformed modular Hamiltonian satisfies the generalized entanglement entropy boundary with entanglement chemical potential.

Abstract

From black hole thermodynamics, the Bekenstein bound has been proposed as a universal thermal entropy bound. It has been further generalized to an entanglement entropy bound which is valid even in a quantum system. In a quantumly entangled system, the non-negativity of the relative entropy leads to the entanglement entropy bound. When the entanglement entropy bound is saturated, a quantum system satisfies the thermodynamics-like law with an appropriately defined entanglement temperature. We show that the saturation of the entanglement entropy bound accounts for a universal feature of the entanglement temperature proportional to the inverse of the system size. In addition, we show that the deformed modular Hamiltonian under a global quench also satisfies the generalized entanglement entropy boundary after introducing a new quantity called the entanglement chemical potential.