Next Article in Journal
About the Concept of Quantum Chaos
Previous Article in Journal
Fractional Diffusion in a Solid with Mass Absorption
Previous Article in Special Issue
Spacetime Topology and the Laws of Black Hole-Soliton Mechanics
Article Menu
Issue 5 (May) cover image

Export Article

Open AccessArticle
Entropy 2017, 19(5), 207; doi:10.3390/e19050207

Coarse Graining Shannon and von Neumann Entropies

1
Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University, 18000 Prague, Czech Republic
2
School of Mathematics and Statistics, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New Zealand
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editor: David Kubiznak
Received: 4 April 2017 / Revised: 27 April 2017 / Accepted: 28 April 2017 / Published: 3 May 2017
(This article belongs to the Special Issue Black Hole Thermodynamics II)
View Full-Text   |   Download PDF [292 KB, uploaded 3 May 2017]

Abstract

The nature of coarse graining is intuitively “obvious”, but it is rather difficult to find explicit and calculable models of the coarse graining process (and the resulting entropy flow) discussed in the literature. What we would like to have at hand is some explicit and calculable process that takes an arbitrary system, with specified initial entropy S, and that monotonically and controllably drives the entropy to its maximum value. This does not have to be a physical process, in fact for some purposes it is better to deal with a gedanken-process, since then it is more obvious how the “hidden information” is hiding in the fine-grain correlations that one is simply agreeing not to look at. We shall present several simple mathematically well-defined and easy to work with conceptual models for coarse graining. We shall consider both the classical Shannon and quantum von Neumann entropies, including models based on quantum decoherence, and analyse the entropy flow in some detail. When coarse graining the quantum von Neumann entropy, we find it extremely useful to introduce an adaptation of Hawking’s super-scattering matrix. These explicit models that we shall construct allow us to quantify and keep clear track of the entropy that appears when coarse graining the system and the information that can be hidden in unobserved correlations (while not the focus of the current article, in the long run, these considerations are of interest when addressing the black hole information puzzle). View Full-Text
Keywords: coarse graining; entropy; information; Shannon entropy; von Neumann entropy coarse graining; entropy; information; Shannon entropy; von Neumann entropy
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Alonso-Serrano, A.; Visser, M. Coarse Graining Shannon and von Neumann Entropies. Entropy 2017, 19, 207.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top