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 us 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.
Physical Review A
- Pub Date:
- May 2018
- Quantum Physics;
- Condensed Matter - Disordered Systems and Neural Networks
- Derivations of Sections IIIA 1-3 were presented in a more transparent way