Universal relation for operator complexity

We study Krylov complexity C-K and operator entropy S-K 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-K similar to lnC(K) 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.

Automated summary

Research has found that there is a logarithmic relation between Krylov complexity and operator entropy in operator growth at long times, which is deeply connected to the irreversibility of operator growth.