2014/09/22 by Ian T. Durham, Ian Durham · 4 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Dynamics #Determinism #Entropy (arrow of time) #Kochen–Specker theorem #Quantum #Quantum Mechanics and Applications #Relation (database) #Statement (logic) #math-ph #math.MP #quant-ph
paper · pdf · doi:10.3390/info5030508
published in Information 5(3), 508-525 (Multidisciplinary Digital Publishing Institute) · Published version; 17 pages, 1 figure; published under title "Quantifying Contextuality" which duplicates another title on the arXiv by different authors
openalex publication_date 2014/09/22 · arxiv created 2014/09/23 · arxiv updated 2014/09/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this essay, I develop order-theoretic notions of determinism and contextuality on domains and topoi. In the process, I develop a method for quantifying contextuality and show that the order-theoretic sense of contextuality is analogous to the sense embodied in the topos-theoretic statement of the Kochen–Specker theorem. Additionally, I argue that this leads to a relation between the entropy associated with measurements on quantum systems and the second law of thermodynamics. The idea that the second law has its origin in the ordering of quantum states and processes dates to at least 1958 and possibly earlier. The suggestion that the mechanism behind this relation is contextuality, is made here for the first time.