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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-03-01
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| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/22/3/322 |
| _version_ | 1811278259077251072 |
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| author | Vitaly Kocharovsky Vladimir Kocharovsky Sergey Tarasov |
| author_facet | Vitaly Kocharovsky Vladimir Kocharovsky Sergey Tarasov |
| author_sort | Vitaly Kocharovsky |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-04-13T00:31:32Z |
| format | Article |
| id | doaj.art-c2c8d27b9c664b6d80f71cf6620bb669 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-13T00:31:32Z |
| publishDate | 2020-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-c2c8d27b9c664b6d80f71cf6620bb6692022-12-22T03:10:27ZengMDPI AGEntropy1099-43002020-03-0122332210.3390/e22030322e22030322Unification of the Nature’s Complexities via a Matrix Permanent—Critical Phenomena, Fractals, Quantum Computing, ♯P-ComplexityVitaly Kocharovsky0Vladimir Kocharovsky1Sergey Tarasov2Department of Physics and Astronomy, Texas A&M University, College Station, TX 77843-4242, USAInstitute of Applied Physics, Russian Academy of Science, Nizhny Novgorod 603950, RussiaInstitute of Applied Physics, Russian Academy of Science, Nizhny Novgorod 603950, RussiaWe 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.https://www.mdpi.com/1099-4300/22/3/322♯p-complexitynp-complexitycritical phenomenafractalsquantum computingmatrix permanentmacmahon master theoremtoeplitz determinant |
| spellingShingle | Vitaly Kocharovsky Vladimir Kocharovsky Sergey Tarasov Unification of the Nature’s Complexities via a Matrix Permanent—Critical Phenomena, Fractals, Quantum Computing, ♯P-Complexity Entropy ♯p-complexity np-complexity critical phenomena fractals quantum computing matrix permanent macmahon master theorem toeplitz determinant |
| 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 | ♯p-complexity np-complexity critical phenomena fractals quantum computing matrix permanent macmahon master theorem toeplitz determinant |
| url | https://www.mdpi.com/1099-4300/22/3/322 |
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