Thermodynamics and area in Minkowski space: Heat capacity of entanglement

Details Thermodynamics and area in Minkowski space: Heat capacity of entanglement Thermodynamics and area in Minkowski space: Heat capacity of entanglement

2003-11-04

arxiv.org/abs/hep-th/0311029v1

Phys.Rev. D69 (2004) 064013

Physics

High Energy Physics

High Energy Physics - Theory

17 pages

Scientific paper

10.1103/PhysRevD.69.064013

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.

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