Hamiltonian mechanics is conservation of information entropy
arXiv:2004.11569 · doi:10.1016/j.shpsb.2020.04.004
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.
25 pages, accepted for publication in Studies in History and Philosophy of Modern Physics