Bernhard Baumgartner

A detailed list of postulates is formulated in an algebraic setting. These postulates are sufficient to entail the standard time evolution governed by the Schrödinger or Dirac equation. They are also necessary in a strong sense: Dropping any one of the postulates allows for other types of time evolution, as is demonstrated with examples. Some philosophical remarks hint on possible further investigations.

A new axiomatic characterization with a minimum of conditions for entropy as a function on the set of states in quantum mechanics is presented. Traditionally unspoken assumptions are unveiled and replaced by proven consequences of the axioms. First the Boltzmann–Planck formula is derived. Building on this formula, using the Law of Large Numbers—a basic theorem of probability theory—the von Neumann formula is deduced. Axioms used in older theories on the foundations are now derived facts.