Liouville dynamics and the conservation of classical information

The invariance of entropic distances under Liouville dynamics yields classical analogues of information-related, quantum mechanical impossible operations. A connection between classically forbidden operations and statistical estimation theory was established by recoursing Fisher's information. Exploring classical analogues of the alluded theorems help to distinguish between their essential quantum mechanical features and aspects that may rise within probabilistic settings. The inquiry contributes to a deeper understanding of the relationship between classical and quantum mechanics.