TL;DR
This paper uncovers a universal logarithmic relation between Krylov complexity and operator entropy in various quantum systems, linking it to irreversibility and operator growth dynamics.
Contribution
It reveals a universal logarithmic relation between operator entropy and complexity across different systems, highlighting its connection to irreversibility in operator growth.
Findings
Logarithmic relation $S_K o ext{log} C_K$ in chaotic and integrable systems
Relation holds at long times, indicating dissipative behavior
Universality linked to irreversibility of operator growth
Abstract
We study Krylov complexity and operator entropy in operator growth. We find that for a variety of systems, including chaotic ones and integrable theories, the two quantities always enjoy a logarithmic relation at long times, where dissipative behavior emerges in unitary evolution. Otherwise, the relation does not hold any longer. Universality of the relation is deeply connected to irreversibility of operator growth.
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