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Journal articles on the topic 'Statistical Symmetries'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Green, HS. "Statistical Symmetries in Physics." Australian Journal of Physics 47, no. 2 (1994): 109. http://dx.doi.org/10.1071/ph940109.

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Every law of physics is invariant under some group of transformations and is therefore the expression of some type of symmetry. Symmetries are classified as geometrical, dynamical or statistical. At the most fundamental level, statistical symmetries are expressed in the field theories of the elementary particles. This paper traces some of the developments from the discovery of Bose statistics, one of the two fundamental symmetries of physics. A series of generalizations of Bose statistics is described. A supersymmetric generalization accommodates fermions as well as bosons, and further general

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2

Aubry, Nadine, and Ricardo Lima. "Spatiotemporal and statistical symmetries." Journal of Statistical Physics 81, no. 3-4 (1995): 793–828. http://dx.doi.org/10.1007/bf02179258.

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3

Pocheau, A. "Scale ratios, statistical symmetries and intermittency." Europhysics Letters (EPL) 43, no. 4 (1998): 410–15. http://dx.doi.org/10.1209/epl/i1998-00103-6.

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4

SAMANI, K. AGHABABAEI, and A. MOSTAFAZADEH. "ON THE STATISTICAL ORIGIN OF TOPOLOGICAL SYMMETRIES." Modern Physics Letters A 17, no. 03 (2002): 131–40. http://dx.doi.org/10.1142/s0217732302006254.

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We investigate a quantum system possessing a parasupersymmetry of order 2, an orthosupersymmetry of order p, a fractional supersymmetry of order p+1, and topological symmetries of type (1,p) and (1,1,…,1). We obtain the corresponding symmetry generators, explore their relationship, and show that they may be expressed in terms of the creation and annihilation operators for an ordinary boson and orthofermions of order p. We give a realization of parafermions of order 2 using orthofermions of arbitrary order p, discuss a p=2 parasupersymmetry between p = 2 parafermions and parabosons of arbitrary

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5

Luque, Amalia, Alejandro Carrasco, Alejandro Martín, and Juan Ramón Lama. "Exploring Symmetry of Binary Classification Performance Metrics." Symmetry 11, no. 1 (2019): 47. http://dx.doi.org/10.3390/sym11010047.

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Selecting the proper performance metric constitutes a key issue for most classification problems in the field of machine learning. Although the specialized literature has addressed several topics regarding these metrics, their symmetries have yet to be systematically studied. This research focuses on ten metrics based on a binary confusion matrix and their symmetric behaviour is formally defined under all types of transformations. Through simulated experiments, which cover the full range of datasets and classification results, the symmetric behaviour of these metrics is explored by exposing th

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6

Olver, Peter J., Jan A. Sanders, and Jing Ping Wang. "Ghost Symmetries." Journal of Nonlinear Mathematical Physics 9, sup1 (2002): 164–72. http://dx.doi.org/10.2991/jnmp.2002.9.s1.14.

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7

Babelon, Olivier, and Denis Bernard. "Dressing symmetries." Communications in Mathematical Physics 149, no. 2 (1992): 279–306. http://dx.doi.org/10.1007/bf02097626.

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8

Giraud, B. G. "Symmetries of independent statistical observables for ultrametric populations." Physical Review E 62, no. 3 (2000): 4450–53. http://dx.doi.org/10.1103/physreve.62.4450.

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9

Deffner, Sebastian, and Wojciech H. Zurek. "Foundations of statistical mechanics from symmetries of entanglement." New Journal of Physics 18, no. 6 (2016): 063013. http://dx.doi.org/10.1088/1367-2630/18/6/063013.

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10

OBERLACK, Martin, Marta WACŁAWCZYK, Andreas ROSTECK, and Victor AVSARKISOV. "Symmetries and their importance for statistical turbulence theory." Mechanical Engineering Reviews 2, no. 2 (2015): 15–00157. http://dx.doi.org/10.1299/mer.15-00157.

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11

Alcaraz, Francisco C., Laurence Jacobs, and Robert Savit. "Classification scheme for statistical theories with unusual symmetries." Nuclear Physics B 257 (January 1985): 340–50. http://dx.doi.org/10.1016/0550-3213(85)90349-9.

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12

Wu, Xiao-Chuan, Wenjie Ji, and Cenke Xu. "Categorical symmetries at criticality." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 7 (2021): 073101. http://dx.doi.org/10.1088/1742-5468/ac08fe.

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13

Petoukhov, Sergey V., and Vitaly I. Svirin. "Binary-genomic numbers and symmetrical regularities in the statistical organization of genomic DNAs." Symmetry: Culture and Science 35, no. 4 (2024): 469–91. https://doi.org/10.26830/symmetry_2024_4_469.

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The article presents new phenomenological regularities of symmetric types in statistical organization of information sequences of single-stranded DNAs in genomes of higher and lower organisms. Binary representations of these DNAs, based on binary-opposition structures in molecular DNA alphabets, are studied. These binary representations of genomic DNAs, which are called binary-genomic numbers (BG-numbers), define huge binary numbers with millions of bits. It is revealed that statistical (probability) organization of BG-numbers possesses internal mirror and fractal-like dichotomous symmetries.

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14

Nucci, M. C. "Lie symmetries of a Painlevé-type equation without Lie symmetries." Journal of Nonlinear Mathematical Physics 15, no. 2 (2008): 205–11. http://dx.doi.org/10.2991/jnmp.2008.15.2.7.

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15

Morando, Paola. "Reduction by λ –symmetries and σ –symmetries: a Frobenius approach". Journal of Nonlinear Mathematical Physics 22, № 1 (2014): 47–59. http://dx.doi.org/10.1080/14029251.2015.996439.

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16

Baake, Michael, and John A. G. Roberts. "Symmetries and reversing symmetries of toral automorphisms." Nonlinearity 14, no. 4 (2001): R1—R24. http://dx.doi.org/10.1088/0951-7715/14/4/201.

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17

Gr$agrave$cia, Xavier, and Josep M. Pons. "Symmetries and infinitesimal symmetries of singular differential equations." Journal of Physics A: Mathematical and General 35, no. 24 (2002): 5059–77. http://dx.doi.org/10.1088/0305-4470/35/24/306.

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18

Junker, Georg. "Special Issue: “Symmetries in Quantum Mechanics and Statistical Physics”." Symmetry 13, no. 11 (2021): 2027. http://dx.doi.org/10.3390/sym13112027.

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19

Zwieback, Simon, and Irena Hajnsek. "Statistical Tests for Symmetries in Polarimetric Scattering Coherency Matrices." IEEE Geoscience and Remote Sensing Letters 11, no. 1 (2014): 308–12. http://dx.doi.org/10.1109/lgrs.2013.2257160.

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20

Mignemi, S. "Asymptotic symmetries and statistical entropy of 2-dimensional gravity." Nuclear Physics B - Proceedings Supplements 88, no. 1-3 (2000): 283–86. http://dx.doi.org/10.1016/s0920-5632(00)00786-6.

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21

Morse, Peter K., and Eric I. Corwin. "Hidden symmetries in jammed systems." Journal of Statistical Mechanics: Theory and Experiment 2016, no. 7 (2016): 074009. http://dx.doi.org/10.1088/1742-5468/2016/07/074009.

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22

Andreanov, A., A. Scardicchio, and S. Torquato. "Extreme lattices: symmetries and decorrelation." Journal of Statistical Mechanics: Theory and Experiment 2016, no. 11 (2016): 113301. http://dx.doi.org/10.1088/1742-5468/2016/11/113301.

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23

Gomes, Pedro R. S. "Aspects of emergent symmetries." International Journal of Modern Physics A 31, no. 10 (2016): 1630009. http://dx.doi.org/10.1142/s0217751x1630009x.

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These are intended to be review notes on emergent symmetries, i.e. symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some background material and go through more recent problems in field theory, statistical mechanics and condensed matter. These problems illustrate how some important symmetries, such as Lorentz invariance and supersymmetry, usually believed to be fundamental, can arise naturally in low-energy regimes of systems involving a large number of degrees of freedom. The

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24

Grabowski, Janusz, Marek Kuś, and Giuseppe Marmo. "Symmetries, Group Actions, and Entanglement." Open Systems & Information Dynamics 13, no. 04 (2006): 343–62. http://dx.doi.org/10.1007/s11080-006-9013-3.

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We address several problems concerning the geometry of the space of Hermitian operators on a finite-dimensional Hilbert space, in particular the geometry of the space of density states and canonical group actions on it. For quantum composite systems we discuss and give examples of entanglement measures.

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25

Leach, P. G. L., and S. É. Bouquet. "Symmetries and Integrating Factors." Journal of Nonlinear Mathematical Physics 9, sup2 (2002): 73–91. http://dx.doi.org/10.2991/jnmp.2002.9.s2.7.

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26

Hydon, Peter E. "Self-Invariant Contact Symmetries." Journal of Nonlinear Mathematical Physics 11, no. 2 (2004): 233–42. http://dx.doi.org/10.2991/jnmp.2004.11.2.8.

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27

Davison, A. H., and A. H. Kara. "Symmetries and Differential Forms." Journal of Nonlinear Mathematical Physics 15, sup1 (2008): 36–43. http://dx.doi.org/10.2991/jnmp.2008.15.s1.3.

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28

Nucci, M. C. "Quantizing preserving Noether symmetries." Journal of Nonlinear Mathematical Physics 20, no. 3 (2013): 451–63. http://dx.doi.org/10.1080/14029251.2013.855053.

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29

Catuogno, Pedro José, and Luis Roberto Lucinger. "Random Lie-point symmetries." Journal of Nonlinear Mathematical Physics 21, no. 2 (2014): 149–65. http://dx.doi.org/10.1080/14029251.2014.900984.

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30

Shabat, A. "Discrete symmetries and solitons." Theoretical and Mathematical Physics 99, no. 3 (1994): 783–89. http://dx.doi.org/10.1007/bf01017068.

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31

Bogoyavlenskij, O. I. "Hidden Structure of Symmetries." Communications in Mathematical Physics 254, no. 2 (2004): 479–88. http://dx.doi.org/10.1007/s00220-004-1253-x.

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32

Boalch, Philip P. "Regge and Okamoto Symmetries." Communications in Mathematical Physics 276, no. 1 (2007): 117–30. http://dx.doi.org/10.1007/s00220-007-0328-x.

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33

Howe, P. S., and G. Papadopoulos. "Holonomy groups andW-symmetries." Communications in Mathematical Physics 151, no. 3 (1993): 467–79. http://dx.doi.org/10.1007/bf02097022.

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34

Morchio, G., and F. Strocchi. "Localization and symmetries." Journal of Physics A: Mathematical and Theoretical 40, no. 12 (2007): 3173–87. http://dx.doi.org/10.1088/1751-8113/40/12/s17.

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35

Peierls, R. "Spontaneously broken symmetries." Journal of Physics A: Mathematical and General 24, no. 22 (1991): 5273–81. http://dx.doi.org/10.1088/0305-4470/24/22/011.

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36

Gui-zhang, T. "The Lie algebraic structure of symmetries generated by hereditary symmetries." Journal of Physics A: Mathematical and General 21, no. 9 (1988): 1951–57. http://dx.doi.org/10.1088/0305-4470/21/9/011.

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37

Lukas, Andre, and Challenger Mishra. "Discrete Symmetries of Complete Intersection Calabi–Yau Manifolds." Communications in Mathematical Physics 379, no. 3 (2020): 847–65. http://dx.doi.org/10.1007/s00220-020-03838-6.

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Abstract In this paper, we classify non-freely acting discrete symmetries of complete intersection Calabi–Yau manifolds and their quotients by freely-acting symmetries. These non-freely acting symmetries can appear as symmetries of low-energy theories resulting from string compactifications on these Calabi–Yau manifolds, particularly in the context of the heterotic string. Hence, our results are relevant for four-dimensional model building with discrete symmetries and they give an indication which symmetries of this kind can be expected from string theory. For the 1695 known quotients of compl

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38

Clark, Timothy T., and Charles Zemach. "Symmetries and the approach to statistical equilibrium in isotropic turbulence." Physics of Fluids 10, no. 11 (1998): 2846–58. http://dx.doi.org/10.1063/1.869806.

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39

Pocheau, A. "The significant digit law: a paradigm of statistical scale symmetries." European Physical Journal B 49, no. 4 (2006): 491–511. http://dx.doi.org/10.1140/epjb/e2006-00084-2.

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40

French, J. B., V. K. B. Kota, A. Pandey, and S. Tomsovic. "Statistical properties of many-particle spectra V. Fluctuations and symmetries." Annals of Physics 181, no. 2 (1988): 198–234. http://dx.doi.org/10.1016/0003-4916(88)90165-0.

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41

Korepanov, I. G. "Hidden symmetries in the 6-vertex model of statistical physics." Journal of Mathematical Sciences 85, no. 1 (1997): 1661–70. http://dx.doi.org/10.1007/bf02355327.

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42

Bookstein, Fred L. "The Inappropriate Symmetries of Multivariate Statistical Analysis in Geometric Morphometrics." Evolutionary Biology 43, no. 3 (2016): 277–313. http://dx.doi.org/10.1007/s11692-016-9382-7.

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43

Pethukov, Sergey V. "Symmetries of Probabilities in Universal Statistical Rules of Genomic DNAs." Symmetry: Culture and Science 35, no. 3 (2024): 263–66. https://doi.org/10.26830/symmetry_2024_3_263.

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44

Chbili, Nafaa, Noura Alderai, Roba Ali, and Raghd AlQedra. "Tutte Polynomials and Graph Symmetries." Symmetry 14, no. 10 (2022): 2072. http://dx.doi.org/10.3390/sym14102072.

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The Tutte polynomial is an isomorphism invariant of graphs that generalizes the chromatic and the flow polynomials. This two-variable polynomial with integral coefficients is known to carry important information about the properties of the graph. It has been used to prove long-standing conjectures in knot theory. Furthermore, it is related to the Potts and Ising models in statistical physics. The purpose of this paper is to study the interaction between the Tutte polynomial and graph symmetries. More precisely, we prove that if the automorphism group of the graph G contains an element of prime

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45

Baake, Michael, and John A. G. Roberts. "Symmetries and reversing symmetries of polynomial automorphisms of the plane." Nonlinearity 18, no. 2 (2004): 791–816. http://dx.doi.org/10.1088/0951-7715/18/2/017.

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46

GAETA, GIUSEPPE. "TWISTED SYMMETRIES OF DIFFERENTIAL EQUATIONS." Journal of Nonlinear Mathematical Physics 16, sup1 (2009): 107–36. http://dx.doi.org/10.1142/s1402925109000352.

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47

Nikitin, Anatolii. "Non-Lie Symmetries and Supersymmetries." Journal of Nonlinear Mathematical Physics 2, no. 3-4 (1995): 405–15. http://dx.doi.org/10.2991/jnmp.1995.2.3-4.21.

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48

Damianou, Pantelis A., and Paschalis G. Paschali. "Symmetries of Maxwell-Bloch Equations." Journal of Nonlinear Mathematical Physics 2, no. 3-4 (1995): 269–77. http://dx.doi.org/10.2991/jnmp.1995.2.3-4.6.

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49

Parasyuk, Ihor. "Symplectic Symmetries of Hamiltonian Systems." Journal of Nonlinear Mathematical Physics 2, no. 3-4 (1995): 278–82. http://dx.doi.org/10.2991/jnmp.1995.2.3-4.7.

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50

Gazizov, Rafail K. "Lie Algebras of Approximate Symmetries." Journal of Nonlinear Mathematical Physics 3, no. 1-2 (1996): 96–101. http://dx.doi.org/10.2991/jnmp.1996.3.1-2.9.

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