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We investigate about exponential convergence for generic quantum Markov semigroups using an generalization of the Lipschitz seminorm and a noncommutative analogue of Wasserstein distance. We show turns out to be closely related with classical convergence rate of reductions to diagonal subalgebras of the given generic quantum Markov semigroups.In particular we compute the convergence rates of generic quantum Markov semigroups. AMS Subject Classification: 81S22, 60J27

ON EXPONENTIAL CONVERGENCE OF GENERIC QUANTUM MARKOV SEMIGROUPS IN A WASSERSTEIN-TYPE DISTANCE