Thermodynamical Property of Entanglement Entropy for Excited States

TL;DR

This paper demonstrates that for small subsystems, entanglement entropy behaves thermodynamically when excited, with an effective temperature inversely proportional to subsystem size, revealing a universal energy-information relationship.

Contribution

It introduces a thermodynamics-like law for entanglement entropy in excited states and confirms this universality through holography and two-dimensional field theories.

Findings

Entanglement entropy obeys a first-law-like relation in excited states.

Effective temperature is proportional to the inverse of subsystem size.

Universal link between energy and quantum information is established.

Abstract

We argue that the entanglement entropy for a very small subsystem obeys a property which is analogous to the first law of thermodynamics when we excite the system. In relativistic setups, its effective temperature is proportional to the inverse of the subsystem size. This provides a universal relationship between the energy and the amount of quantum information. We derive the results using holography and confirm them in two dimensional field theories. We will also comment on an example with negative specific heat and suggest a connection between the second law of thermodynamics and the strong subadditivity of entanglement entropy.