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A principle of information conservation is shown in abstract terms to ruleout probabilistic physical laws, necessitating the existence of statetrajectories. It furthermore provides a geometric-thermodynamic mechanism forthe appearance of probability distributions at the operational level, and thusmay provide a dynamical explanation for Born's rule of quantum probabilities.This link between geometry and operational probabilities is argued to be apromising angle from which to study the potential for "hidden information" inquantum systems, and guide efforts in quantum foundations more generally.

A principle of information conservation for physical laws (Hidden information in quantum systems?)