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We provide an upper bound on the maximal entropy rate at which the entropy ofthe expected density operator of a given ensemble of two states changes undernonlocal unitary evolution. A large class of entropy measures in considered,which includes Renyi and Tsallis entropies. The result is derived from ageneral bound on the trace-norm of a commutator, which can be expected to findother implementations. We apply this result to bound the maximal rate at whichquantum dynamics can generate entanglement in a bipartite closed system withRenyi and Tsallis entanglement entropy taken as measures of entanglement in thesystem.

Entanglement rates for Renyi, Tsallis and other entropies