Characterizing Entropy in Statistical Physics and in Quantum Information Theory

被引：0

作者：

Bernhard Baumgartner

机构：

[1] Universität Wien,Institut für Theoretische Physik

来源：

Foundations of Physics | 2014年 / 44卷

关键词：

Entropy; Axiomatic; Information; Large numbers; 94A17;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

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.

引用

页码：1107 / 1123

页数：16

共 22 条

[1]

Åberg J(2013)Truly work-like work extraction via a single-shot analysis Nat. Commun. 4 1925-146

[2]

Aczél J(1974)Why the Shannon and Hartley entropies are ‘Natural’ Adv. Appl. Probab. 6 131-18

[3]

Forte B(2010)Landauer’s principle in the quantum domain Electron. Proc. Theor. Comput. Sci. 26 13-828

[4]

Ng CT(1914)Beiträge zur Quantentheorie Verh. Deutsch. Phys. Ges. 12 820-549

[5]

Anders J(2007)An information-spectrum approach to classical and quantum hypothesis testing for simple hypotheses IEEE Trans. Inf. Theory 53 534-120

[6]

Shabbir S(1975)A new axiomatic characterization of the von Neumann entropy Rep. Math. Phys. 3 109-563

[7]

Hilt S(1901)Über das Gesetz der Energieverteilung im Normalspektrum Ann. Phys. 4 553-5847

[8]

Lutz E(2009)A fully quantum asymptotic equipartition property IEEE Trans. Inf. Theory 55 5840-637

[9]

Einstein A(1971)Sätze über Dichtematrizen Wiss. Z. Karl-Marx-Univ. 20 633-452

[10]

Nagaoka H(1972)Wiss. Z. Karl-Marx-Univ. Endlich-dimensionale Dichtematrizen I 21 421-177

← 1 2 3 →