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# Markov shift in non-commutative probability

@inproceedings{MohariMarkovSI, title={Markov shift in non-commutative probability}, author={Anilesh Mohari and Surendra Nath Bose} }

We consider a class of quantum dissipative semigroup on a von-Neumann algebra which admits a normal invariant state. We investigate asymptotic behavior of the dis-sipative dynamics and their relation to that of the canonical Markov shift. In case the normal invariant state is also faithful, we also extend the notion of 'quantum detailed balance' introduced by Frigerio-Gorini and prove that forward weak Markov process and backward weak Markov process are equivalent by an anti-unitary operator.