Thermodynamics and area in Minkowski space: Heat capacity of entanglement

TL;DR

This paper explores how quantum fluctuations in Minkowski space relate to thermodynamic properties like heat capacity, revealing area scaling behavior and its implications for entanglement and spacetime geometry.

Contribution

It demonstrates the connection between quantum fluctuations and thermodynamic quantities in Minkowski space, extending area scaling insights beyond simple geometries.

Findings

Quantum fluctuations scale linearly with surface area.

Area scaling of thermodynamic quantities is derived from quantum fluctuations.

Interpretation as a canonical ensemble is limited to specific geometries.

Abstract

Tracing over the degrees of freedom inside (or outside) a sub-volume V of Minkowski space in a given quantum state |psi>, results in a statistical ensemble described by a density matrix rho. This enables one to relate quantum fluctuations in V when in the state |psi>, to statistical fluctuations in the ensemble described by rho. These fluctuations scale linearly with the surface area of V. If V is half of space, then rho is the density matrix of a canonical ensemble in Rindler space. This enables us to `derive' area scaling of thermodynamic quantities in Rindler space from area scaling of quantum fluctuations in half of Minkowski space. When considering shapes other than half of Minkowski space, even though area scaling persists, rho does not have an interpretation as a density matrix of a canonical ensemble in a curved, or geometrically non-trivial, background.