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...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-03-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/22/3/322 |
| Summary: | 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. |
|---|---|
| ISSN: | 1099-4300 |