We shortly review the progress in the domain of stochastic dynamics for quantum spin systems on a lattice. We also present some new results obtained in the framework of noncommutative [Formula: see text] spaces. In particular, using noncommutative Radon-Nikodym theorem of A. Connes we construct Markov generators of stochastic dynamics of spin flip type for systems at high temperatures or on one-dimensional lattice and with interactions of finite range at arbitrary temperatures.
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