Foundations of Physics 44 (10):1107-1123 (2014)

Abstract
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
Keywords Entropy  Axiomatic  Information  Large numbers
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DOI 10.1007/s10701-014-9832-y
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A Mathematical Theory of Communication.Claude E. Shannon - 1948 - Bell System Technical Journal 27:379–423.

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