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A conjecture for the universal constraints for relaxation rates of a quantumdynamical semigroup is proposed. It is shown that it holds for severalinteresting classes of semigroups, e.g. unital semigroups and semigroupsderived in the weak coupling limit from the proper microscopic model. Moreover,proposed conjecture is supported by numerical analysis. This conjecture hasseveral important implications: it allows to provide universal constraints forspectra of quantum channels and provides necessary condition to decide whethera given channel is consistent with Markovian evolution.

On the universal constraints for relaxation rates for quantum dynamical semigroup