Bernoulli property of equilibrium states for certain partially hyperbolic diffeomorphisms

Kolmogorov-Bernoulli equivalence is a classical problem in ergodic theory. We consider topologically transitive partially hyperbolic diffeomorphisms with Lyapunov stable center direction. There exists a unique equilibrium state for any potential function satisfying Bowen property, by Climenhaga-Pesin-Zelerowicz. In this talk, we show that when the system is topologically mixing, the unique equilibrium state has the Kolmogorv property. Then we lift the Kolmogorv property to the Bernoulli property using Ornstein-Weiss theory.