22.05.2024 (Wednesday)

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

Regular Seminar Markus Froeb (U. Leipzig)

13:00 KCL
room S0.12

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 give a short introduction to Tomita--Takesaki modular theory and present examples of modular Hamiltonians. Using these, I will give results for therelative entropy between the de Sitter vacuum state and a coherent excitation thereof in diamond and wedge regions, and show explicitly that the result satisfies the expected properties for a relative entropy. Finally, I will use local thermodynamic laws to determine the local temperature that is measured by an observer, and consider the backreaction of the quantum state on the geometry to prove an entropy-area law for de Sitter spacetime. Based on arXiv:arXiv:2308.14797, 2310.12185, 2311.13990 and 2312.04629.