Hamiltonian mechanics is conservation of information entropy. (August 2020) - Carcassi, Gabriele; Aidala, Christine A.
Abstract: In this work we show the equivalence between Hamiltonian mechanics and conservation of information entropy. We will show that distributions with coordinate independent values for information entropy require that the manifold on which the distribution is defined is charted by conjugate pairs (i.e. it is a symplectic manifold). We will also show that further requiring that the information entropy is conserved during the evolution yields Hamilton's equations. Highlights: Hamiltonian dynamics is deterministic/reversible evolution of invariant distributions. Coordinate-invariant information entropy can only be defined on symplectic manifolds. Conservation of information entropy leads to symplectomorphism.