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