Foundations of Physics

, Volume 44, Issue 10, pp 1107–1123 | Cite as

Characterizing Entropy in Statistical Physics and in Quantum Information Theory

Article

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 

Mathematics Subject Classification

94A17 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikUniversität WienViennaAustria

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