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 ...

Laplacian and D’Alembertian operators on functions are very important tools for several branches of Mathematics and Physics. In addition to their relevance, both operators are very used in vector calculus. In this paper, we show a relationship between the Laplacian and the D’Alembertian operators, not only on functions but also on vector fields defined on hypersurfaces in the m-dimensional Lore...