Entropy of Bogoliubov automorphisms of CAR and CCR algebras with respect to quasi-free states

TL;DR

This paper calculates the dynamical entropy of Bogoliubov automorphisms in CAR and CCR algebras with respect to gauge-invariant quasi-free states, advancing the understanding of quantum dynamical systems.

Contribution

It completes the calculation of dynamical entropy for these automorphisms, building on prior foundational work by Stormer, Voiculescu, Narnhofer-Thirring, and Park-Shin.

Findings

Dynamical entropy computed for Bogoliubov automorphisms in CAR and CCR algebras.

Results extend previous research, providing a comprehensive understanding of gauge-invariant quasi-free states.

Advances the theoretical framework of quantum dynamical entropy.

Abstract

We compute the dynamical entropy of Bogoliubov automorphisms of CAR and CCR algebras with respect to arbitrary gauge-invariant quasi-free states. This completes the research started by Stormer and Voiculescu, and continued in works of Narnhofer-Thirring and Park-Shin.