Reformulating Classical Mechanics with Non-Hermitian Operators

Entanglement is often considered exclusive to quantum mechanics, yet we demonstrate that it also emerges in classical mechanics, particularly in the center-of-mass system. However, unlike quantum entanglement, where all orthogonal states carry physical significance, classical entanglement does not necessarily imply the meaningfulness of orthogonal states. Here, we reconstruct the laws of classical mechanics using an operator-based framework and reveal its inherent reliance on non-Hermitian operators. This challenges the conventional notion of a space-spanning basis of states, explaining why classical mechanics identifies individual states rather than a complete orthogonal set.