Quantum Coarse-Graining, Symmetries and Reducibility of Dynamics

The common idea behind complexity reduction in physical systems is separation of information into "physically meaningful" and "safely ignorable". Here we consider a generic notion of such separation -- implemented by coarse-graining the state-space -- and address the question of what information is indeed safely ignorable if we want to reduce the complexity of dynamics. The general condition for reducibility of dynamics under coarse-graining will be presented for stochastic and quantum systems. In the process we develop the quantum notion of state-space coarse-graining that allows to marginalize selected degrees of freedom. One of our main findings is that there is a broader class of symmetries, beyond those that are considered by Noether's Theorem, that can play a role in the reduction of dynamics. Some examples of quantum coarse-grainings and the reduction of dynamics with symmetries will be discussed.