Notions of Fermionic Entropies of a Causal Fermion System

TL;DR

This paper introduces and explores various notions of fermionic entropies within causal fermion systems, illustrating their properties through examples in different spacetime geometries and connecting to modular theory.

Contribution

It defines fermionic entropies for causal fermion systems using quasi-free fermionic states and demonstrates their application in diverse physical scenarios.

Findings

Fermionic entropies are explicitly defined for causal fermion systems.

Area laws are reviewed for specific spacetime regions.

Connections to modular theory are established for computing relative entropy.

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.