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Explore bimodule quantum Markov semigroups and their role in describing quantum system dynamics that preserve symmetries in this mathematical physics seminar. Delve into how symmetries are encoded through finite index inclusions of von Neumann algebras N⊆M and extracted from standard invariants of these inclusions. Learn how generators of bimodule quantum Markov semigroups can be expressed using Fourier multipliers through the standard invariant framework. Discover the extended concept of bimodule equilibrium states, which generalizes traditional equilibrium states and allows quantum channels to admit equilibrium even without stationary states. Examine the mathematical structure showing that when bimodule quantum channels admit bimodule equilibrium, their fixed points form von Neumann subalgebras of M. Investigate how classical functional inequalities including the Poincaré inequality, logarithmic Sobolev inequality, and Talagrand inequality extend to bimodule equilibrium settings, providing new tools for analyzing quantum systems with symmetry constraints.
