The growth of operator entropy in operator growth

A bstract We study upper bounds on the growth of operator entropy S K in growth. Using uncertainty relation, we first prove a dispersion bound rate |∂ t | ≤ 2 b 1 ∆ , where is Lanczos coefficient and variance . However, for irreversible process, this generally turns out to be too loose at long times. further find tighter time limit using universal logarithmic relation between Krylov complexity entropy. The new describes behavior very well physically interesting cases, such as chaotic systems integrable models.