Liouville's Theorem does indeed seem to imply that entropy doesn't change: https://physics.stackexchange.com/questions/202522/how-is-liouvilles-theorem-compati

Liouville's Theorem does indeed seem to imply that entropy doesn't change: https://physics.stackexchange.com/questions/202522/how-is-liouvilles-theorem-compatible-with-the-second-law https://physics.stackexchange.com/questions/202522/how-is-li...