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2022

The growth of operator entropy in operator growth

Fan, Zhong-Ying

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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 $|\partial_t S_K|\leq 2b_1 \Delta S_K$, where $b_1$ is the first Lanczos coefficient and $\Delta S_K$ 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 entropy.

The growth of operator entropy in operator growth · Around

Built on

J. L. F. Barbón, E. Rabinovici, R. Shir and R. Sinha, On The Evolution Of Operator Complexity Beyond Scrambling,
Original
1907
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Ernest R. Davidson, On derivations of the uncertainty principle
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M. H. Lee, J. Florencio, and J. Hong, Dynamic equivalence of a two-dimensional quantum electron gas and a classical harmonic oscillator chain with an impurity mass
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M. Howard Lee, Ergodic Theory, Infinite Products, and Long Time Behavior in Hermitian Models
2001
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