A Noether Theorem for Markov Processes

Details A Noether Theorem for Markov Processes A Noether Theorem for Markov Processes

2012-03-09

arxiv.org/abs/1203.2035v1

Physics

Mathematical Physics

9 pages

Scientific paper

Noether's theorem links the symmetries of a quantum system with its conserved quantities, and is a cornerstone of quantum mechanics. Here we prove a version of Noether's theorem for Markov processes. In quantum mechanics, an observable commutes with the Hamiltonian if and only if its expected value remains constant in time for every state. For Markov processes that no longer holds, but an observable commutes with the Hamiltonian if and only if both its expected value and standard deviation are constant in time for every state.

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