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We study Krylov complexity C₊ and operator entropy S₊ 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 S₊C₊ 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.
Zhong-Ying Fan (Thu,) studied this question.
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