Next Article in Journal
Entropy Generation Assessment for Wall-Bounded Turbulent Shear Flows Based on Reynolds Analogy Assumptions
Previous Article in Journal
Sample Entropy Combined with the K-Means Clustering Algorithm Reveals Six Functional Networks of the Brain
Previous Article in Special Issue
Reduced Data Sets and Entropy-Based Discretization
Open AccessArticle

Möbius Transforms, Cycles and q-triplets in Statistical Mechanics

Astroparticles and Cosmology (UMR 7164), Sorbonne Paris Cité, Univ Paris Diderot, 75205 Paris, France
Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology of Complex Systems, Rua Xavier Sigaud 150, Rio de Janeiro 22290-180, Brazil
Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
Complexity Science Hub Vienna, Josefstädter Strasse 39, 1080 Vienna, Austria
Author to whom correspondence should be addressed.
Entropy 2019, 21(12), 1155;
Received: 24 October 2019 / Revised: 21 November 2019 / Accepted: 22 November 2019 / Published: 26 November 2019
(This article belongs to the Special Issue The Ubiquity of Entropy)
In the realm of Boltzmann-Gibbs (BG) statistical mechanics and its q-generalisation for complex systems, we analysed sequences of q-triplets, or q-doublets if one of them was the unity, in terms of cycles of successive Möbius transforms of the line preserving unity ( q = 1 corresponds to the BG theory). Such transforms have the form q ( a q + 1 a ) / [ ( 1 + a ) q a ] , where a is a real number; the particular cases a = 1 and a = 0 yield, respectively, q ( 2 q ) and q 1 / q , currently known as additive and multiplicative dualities. This approach seemingly enables the organisation of various complex phenomena into different classes, named N-complete or incomplete. The classification that we propose here hopefully constitutes a useful guideline in the search, for non-BG systems whenever well described through q-indices, of new possibly observable physical properties. View Full-Text
Keywords: non-additive entropy; q-statistics; Möbius transform; complex systems non-additive entropy; q-statistics; Möbius transform; complex systems
MDPI and ACS Style

Gazeau, J.P.; Tsallis, C. Möbius Transforms, Cycles and q-triplets in Statistical Mechanics. Entropy 2019, 21, 1155.

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.

Article Access Map by Country/Region

Back to TopTop