Information 2014, 5(3), 508-525; https://doi.org/10.3390/info5030508
An Order-Theoretic Quantification of Contextuality
Department of Physics, Saint Anselm College, 100 Saint Anselm Drive, Manchester, NH 03102, USA
Received: 15 May 2014 / Revised: 16 September 2014 / Accepted: 16 September 2014 / Published: 22 September 2014
(This article belongs to the Special Issue Physics of Information)
Abstract
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. View Full-TextKeywords:
contextuality; entropy; domain theory; topos theory; category theory; second law of thermodynamics; determinism
▼
Figures
Figure 1
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
Share & Cite This Article
MDPI and ACS Style
Durham, I.T. An Order-Theoretic Quantification of Contextuality. Information 2014, 5, 508-525.
Related Articles
Article Metrics
Comments
[Return to top]
Information
EISSN 2078-2489
Published by MDPI AG, Basel, Switzerland
RSS
E-Mail Table of Contents Alert