# The growth of operator entropy in operator growth

@article{Fan2022TheGO, title={The growth of operator entropy in operator growth}, author={Zhong Fan}, journal={Journal of High Energy Physics}, year={2022}, volume={2022}, pages={1-16} }

We study upper bounds on the growth of operator entropy S K in operator growth. Using uncertainty relation, we first prove a dispersion bound on the growth rate |∂ t S K | ≤ 2 b 1 ∆ S K , where b 1 is the first Lanczos coefficient and ∆ S K is the variance of S K . However, for irreversible process, this bound generally turns out to be too loose at long times. We further find a tighter bound in the long time limit using a universal logarithmic relation between Krylov complexity and operator…

## 2 Citations

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