  In recent years, the non-relativistic quantum dynamics derived from three
assumptions; i) probability current conservation, ii) average energy
conservation, and iii) an epistemic momentum uncertainty [A. Budiyono and D.
Rohrlich, \href{https://doi.org/10.1038/s41467-017-01375-w}{Nat. Commun 8, 1306
(2017)}]. Here we show that, these assumptions can be derived from a natural
extension of classical statistical mechanics.
