Entropy, holography and the second law

TL;DR

This paper explores the properties of entropy in quantum field theory and black holes, highlighting issues with invariance, renormalization, and the impact of particles outside horizons on thermodynamic descriptions.

Contribution

It analyzes the non-invariance of geometric entropy, the effects of renormalization on entropy and energy, and the complications introduced by particles outside horizons in accelerated frames.

Findings

Geometric entropy is not a Lorentz scalar and lacks invariant meaning.

Renormalization can lead to negative free energy without boundary conditions.

Particles outside the horizon affect the Unruh temperature description.

Abstract

The geometric entropy in quantum field theory is not a Lorentz scalar and has no invariant meaning, while the black hole entropy is invariant. Renormalization of entropy and energy for reduced density matrices may lead to the negative free energy even if no boundary conditions are imposed. Presence of particles outside the horizon of a uniformly accelerated observer prevents the description in terms of a single Unruh temperature.