Exponential convergence in the trace norm and time-inhomogeneous Markovian evolutions on ℬ(ℋ)

We consider a sequence of operators [Formula: see text] that describes the time evolution of normal states of an open quantum system. Our objective is to analyze the asymptotic behavior of [Formula: see text], where [Formula: see text] is an arbitrary initial normal state. Our focus is on specific situations in which the operators [Formula: see text] are produced by various quantum Markov semigroups of weak coupling limit-type. To tackle this problem, we introduce a new result concerning exponential convergence to equilibrium in the trace norm for quantum Markov semigroups, provided that their induced semigroups have a spectral gap. Moreover, applications to quantum annealing are discussed.