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Characterizing Entropy in Statistical Physics and in Quantum Information Theory

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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.

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Acknowledgments

The author thanks the referees for important hints, and he gives many thanks to Elliott Lieb and Jakob Yngvason for discussions.

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  1. Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, 1090, Vienna, Austria

    Bernhard Baumgartner

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  1. Bernhard Baumgartner
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Correspondence to Bernhard Baumgartner.

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Baumgartner, B. Characterizing Entropy in Statistical Physics and in Quantum Information Theory. Found Phys 44, 1107–1123 (2014). https://doi.org/10.1007/s10701-014-9832-y

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  • DOI: https://doi.org/10.1007/s10701-014-9832-y

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