Unification of the Nature’s Complexities via a Matrix Permanent—Critical Phenomena, Fractals, Quantum Computing, ♯P-Complexity

We reveal the analytic relations between a matrix permanent and major nature’s complexities manifested in critical phenomena, fractal structures and chaos, quantum information processes in many-body physics, number-theoretic complexity in mathematics, and ♯P-complete problems in the theory of comput...

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Detalles Bibliográficos
Autores principales: Kocharovsky, Vitaly, Kocharovsky, Vladimir, Tarasov, Sergey
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516781/
https://www.ncbi.nlm.nih.gov/pubmed/33286096
http://dx.doi.org/10.3390/e22030322
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author Kocharovsky, Vitaly
Kocharovsky, Vladimir
Tarasov, Sergey
author_facet Kocharovsky, Vitaly
Kocharovsky, Vladimir
Tarasov, Sergey
author_sort Kocharovsky, Vitaly
collection PubMed
description We reveal the analytic relations between a matrix permanent and major nature’s complexities manifested in critical phenomena, fractal structures and chaos, quantum information processes in many-body physics, number-theoretic complexity in mathematics, and ♯P-complete problems in the theory of computational complexity. They follow from a reduction of the Ising model of critical phenomena to the permanent and four integral representations of the permanent based on (i) the fractal Weierstrass-like functions, (ii) polynomials of complex variables, (iii) Laplace integral, and (iv) MacMahon master theorem.
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spelling pubmed-75167812020-11-09 Unification of the Nature’s Complexities via a Matrix Permanent—Critical Phenomena, Fractals, Quantum Computing, ♯P-Complexity Kocharovsky, Vitaly Kocharovsky, Vladimir Tarasov, Sergey Entropy (Basel) Article We reveal the analytic relations between a matrix permanent and major nature’s complexities manifested in critical phenomena, fractal structures and chaos, quantum information processes in many-body physics, number-theoretic complexity in mathematics, and ♯P-complete problems in the theory of computational complexity. They follow from a reduction of the Ising model of critical phenomena to the permanent and four integral representations of the permanent based on (i) the fractal Weierstrass-like functions, (ii) polynomials of complex variables, (iii) Laplace integral, and (iv) MacMahon master theorem. MDPI 2020-03-12 /pmc/articles/PMC7516781/ /pubmed/33286096 http://dx.doi.org/10.3390/e22030322 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Kocharovsky, Vitaly
Kocharovsky, Vladimir
Tarasov, Sergey
Unification of the Nature’s Complexities via a Matrix Permanent—Critical Phenomena, Fractals, Quantum Computing, ♯P-Complexity
title Unification of the Nature’s Complexities via a Matrix Permanent—Critical Phenomena, Fractals, Quantum Computing, ♯P-Complexity
title_full Unification of the Nature’s Complexities via a Matrix Permanent—Critical Phenomena, Fractals, Quantum Computing, ♯P-Complexity
title_fullStr Unification of the Nature’s Complexities via a Matrix Permanent—Critical Phenomena, Fractals, Quantum Computing, ♯P-Complexity
title_full_unstemmed Unification of the Nature’s Complexities via a Matrix Permanent—Critical Phenomena, Fractals, Quantum Computing, ♯P-Complexity
title_short Unification of the Nature’s Complexities via a Matrix Permanent—Critical Phenomena, Fractals, Quantum Computing, ♯P-Complexity
title_sort unification of the nature’s complexities via a matrix permanent—critical phenomena, fractals, quantum computing, ♯p-complexity
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516781/
https://www.ncbi.nlm.nih.gov/pubmed/33286096
http://dx.doi.org/10.3390/e22030322
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