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  4. A Unified treatment of classical probability, thermodynamics, and quantum information theory
 
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A Unified treatment of classical probability, thermodynamics, and quantum information theory

Citation Link: https://doi.org/10.15480/882.3770
Publikationstyp
Book
Date Issued
2021-09-14
Sprache
English
Author(s)
Jansson, Christian  
Institut
Zuverlässiges Rechnen E-19  
TORE-DOI
10.15480/882.3770
TORE-URI
http://hdl.handle.net/11420/10330
Citation
Technische Universität Hamburg (2021)
Peer Reviewed
false
The major goal of these notes is an elaborate presentation of a probabilistic framework. This framework allows a formulation of classical probability theory, thermodynamics, and quantum probability with a common set of four principles or axioms. In particular, it provides a general prognostic algorithm for computing probabilities about future events. Our principles distinguish strictly between possibilities and outcomes. A well-defined possibility space and a sample space of outcomes resolves well-known paradoxes, and make quantum interpretations like ''many worlds`` or ''many minds`` superfluous. In addition, the superposition principle and the entanglement of systems obtain a new meaning from our point of view.

This framework offers an axiomatic approach to probability in the sense of Hilbert. He asked for treating probability axiomatically in his sixth of the twenty-three open problems presented to the International Congress of Mathematicians in Paris in 1900. We have applied our framework to various problems, including classical problems, statistical mechanics and thermodynamics, diffraction at multiple slits, light reflection, interferometer, delayed-choice experiments, and Hardy's Paradox.

Particular emphasis is also placed on C.F. von Weizs\"acker's work, who developed his ur theory as early as the 1950s. Today, leading researchers continue his work under the name ''Simons Collaboration on Quantum Fields, Gravity, and Information``.
Subjects
probability theory
quantum theory
thermodynamics
quantum information theory
entropy
reconstructions
DDC Class
510: Mathematik
Lizenz
https://creativecommons.org/licenses/by/4.0/
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