Generic classification of the quasi-free flows on the Cuntz algebra ${\mathcal{O}}_2$

In this article we show that the quasi-free flows on the Cuntz algebra ${\mathcal{O}}_2$ are generically classifiable by the inverse temperature of their unique KMS state. Along the way, we show that a large class of quasi-free flows on the Cuntz algebra ${\mathcal{O}}_n$ are generically equivariantly $\mathcal{Z}$-stable and their corresponding dual action has the Rokhlin property generically.