Modular Hamiltonians, relative entropy and the entropy-area law in de Sitter spacetime

Abstract: In a very general setting, entropy quantifies the amount of information about a system that an observer has access to. However, in contrast to quantum mechanics, in quantum field theory naive measures of entropy are divergent. To obtain finite results, one needs to consider measures such as relative entropy, which can be computed from the modular Hamiltonian using Tomita--Takesaki theory.

In this talk, I will explain the connection between the quantum-mechanical expressions for (relative) entropy, the modular Hamiltonian and Tomita--Takesaki theory. I then present two examples of modular Hamiltonians that were recently derived: one for conformal fields in diamond regions of conformally flat spacetimes (including de Sitter), and one for fermions of small mass in diamond regions of two-dimensional Minkowski spacetime. I will give results for the relative entropy between the de Sitter vacuum state and a coherent excitation thereof in diamonds and wedges, and show explicitly that the result satisfies the expected properties for a relative entropy. Finally, I will use thermodynamic relations to determine the local temperature that is measured by an observer, and consider the backreaction of the coherent excitation on the geometry to prove an entropy-area law for de Sitter spacetime.

Based on arXiv:2308.14797, 2310.12185, 2311.13990 and 2312.04629.

general relativity and quantum cosmologyHEP - experimentHEP - latticeHEP - phenomenologyHEP - theory

Audience: researchers in the topic

( slides )

---

NKUA HEP Seminars

Series comments: Please email tomeasb(at)gmail(dot)com to obtain the meeting link and password. Unless explicitly requested otherwise, your email address will be included in our seminar mailing list.

---