Notions of Fermionic Entropies for Causal Fermion Systems
Abstract The fermionic von Neumann entropy, the fermionic entanglement entropy and the fermionic relative entropy are defined for causal fermion systems. Our definition makes use of entropy formulas for quasi-free fermionic states in terms of the reduced one-particle density operator. Our definitions are illustrated in various examples for Dirac spinors in two- and four-dimensional Minkowski space, in the Schwarzschild black hole geometry and for fermionic lattices. We review area laws for the two-dimensional diamond and a three-dimensional spatial region in Minkowski space. The connection is made to the computation of the relative entropy using modular theory.
Authors
- Magdalena Lottner
- Robert H. Jonsson (ORCID: https://orcid.org/0000-0003-0295-250X)
- Simone Murro (ORCID: https://orcid.org/0000-0003-3044-5476)
- Felix Finster (ORCID: https://orcid.org/0000-0002-9531-7742)
- Albert Much (ORCID: https://orcid.org/0009-0008-6320-7865)
Institutions
- Stockholm University (SE)
- Istituto Nazionale di Fisica Nucleare, Sezione di Genova (IT)
- University of Regensburg (DE)
- KTH Royal Institute of Technology (SE)
- Leipzig University (DE)
Publication Details
- Journal
- Mathematical Physics Analysis and Geometry
- Published
- 2025-04-15
- DOI
- https://doi.org/10.1007/s11040-025-09505-3
- Citations
- 2
- Primary Topic
- Quantum many-body systems
- Type
- article
- Field-Weighted Citation Impact
- 2.49
Funders
- Wenner-Gren Stiftelserna
- Ministero dell’Istruzione, dell’Università e della Ricerca
- Studienstiftung des Deutschen Volkes
- Università degli Studi di Genova
- NordForsk