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We review the recent results [45, 46] concerning the semiclassical limit fromthe Hartree dynamics to the Vlasov equation with singular potentials and extendthem to the case of more general radial interactions. We prove that, atpositive temperature, the Hartree dynamics converges in trace norm to theVlasov one, for a particular class of initial states.

From the Hartree to the Vlasov dynamics: conditional strong convergence