  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.
