Nonlinearity of the non-Abelian lattice gauge field theory according to the spectrum of Kolmogorov-Sinai entropy and complexity

[1]C. Adami, N. T. Cerf, Physical complexity of symbolic sequences, Physica D 137 (2000) 62–69. ⇒37510.1016/S0167-2789(99)00179-7Search in Google Scholar

[2]C. Anteneodo, A.R. Plastino, Some features of the López-Ruiz-Mancini-Calbet (LMC) statistical measure of complexity Physics Letters A 223 (1996) 348–354. ⇒374, 37510.1016/S0375-9601(96)00756-6Search in Google Scholar

[3]V. Bannur, Statistical mechanics of Yang-Mills classical mechanics, Phys. Rev. C 72 (2005) 024904. ⇒37410.1103/PhysRevC.72.024904Search in Google Scholar

[4]T. S. Biró, C. Gong, B. Müller, A. Trayanov, Hamiltonian dynamics of Yang-Mills fields on a lattice Int. Journ. of Modern Phys. C 5 (1994) 113–149. ⇒38410.1142/S0129183194000106Search in Google Scholar

[5]T. S. Biró, Conserving algorithms for real-time nonabelian lattice gauge theories Int. Journ. of Modern Phys. C6 (1995) 327–344. ⇒38510.1142/S0129183195000241Search in Google Scholar

[6]T. S. Biró, S. G. Matinyan, and B. Müller, Chaos and Gauge Field Theory World Scientific, Singapore, 1995. ⇒38810.1142/2584Search in Google Scholar

[7]T. S. Biro, A. Fülöp, C. Gong, S. Matinyan, B. Müller, A. Trayanov, Chaotic dynamics in classical lattice field theories, Lecture Notes in Physics (1997) 164–176. ⇒38510.1007/BFb0104308Search in Google Scholar

[8]G. Bo etta, M. Cencini, M. Falcioni, A. Vulpiani, Predictability: a way to characterize complexity Phys. Reports 356 (2002) 367–474. ⇒37410.1016/S0370-1573(01)00025-4Search in Google Scholar

[9]J. Bolte, B. Müler, and A. Schafer, Ergodic properties of classical SU(2) lattice gauge theory Phys. Rev. D 61 (2000) 054506. ⇒38910.1103/PhysRevD.61.054506Search in Google Scholar

[10]G. M. Bosyk, S. Zozor, F. Holik, M. Portesi, P. W. A. Lamberti, A family of generalized quantum entropies: Definition and properties Quantum Inf. Process. 15 (2016) 3393–3420. ⇒37510.1007/s11128-016-1329-5Search in Google Scholar

[11]X. Calbet and R. López-Ruiz, Tendency towards maximum complexity in a nonequilibrium isolated system Phys. Rev. E 63 (2001) 066116. ⇒374, 39310.1103/PhysRevE.63.066116Search in Google Scholar

[12]M. Creutz, Gauge fixing, the transfer matrix, and confinement on a lattice Phys. Rev. D 15 (1977) 1128. ⇒37710.1103/PhysRevD.15.1128Search in Google Scholar

[13]J. P. Crutchfield, K. Young, Inferring statistical complexityPhys. Rev. Lett. 63 (1989) 105. ⇒37410.1103/PhysRevLett.63.105Search in Google Scholar

[14]P. A. M. Dirac, On the analogy between classical and quantum mechanics Rev. Mod. Phys. 17 (1945) 195. ⇒37610.1103/RevModPhys.17.195Search in Google Scholar

[15]G.L. Ferri, F. Pennini, A. Plastino, LMC-complexity and various chaotic regimes Physics Letters A 373 (2009) 2210–2214. ⇒37510.1016/j.physleta.2009.04.062Search in Google Scholar

[16]R. P. Feynman, Space-Time Approach to Non-Relativistic Quantum Mechanics, Modern Physics 20. 2 (1948) 367. ⇒37610.1103/RevModPhys.20.367Search in Google Scholar

[17]A. Fülöp, Statistical complexity and generalized number system, Acta Univ. Sapientiae, Informatica 6, 2 (2014) 230–251. ⇒37510.1515/ausi-2015-0006Search in Google Scholar

[18]A. Fülöp, Statistical complexity of the time dependent damped L84 model Chaos 29 (2019) 083105. ⇒37510.1063/1.510751031472508Search in Google Scholar

[19]A. Fülöp, T. S. Biró, Towards the equation of state of a classical SU(2) lattice gauge theory, Phys. Rev. C 64 (2001) 064902. ⇒374, 386, 387, 388, 38910.1103/PhysRevC.64.064902Search in Google Scholar

[20]P. Grassberger, Toward a quantitative theory of self-generated complexity Int. Journ. Theor. Phys. 25 (1986) 907–938. ⇒37410.1007/BF00668821Search in Google Scholar

[21]C. Gong, Lyapunov spectra in SU(2) lattice gauge theory Phys. Rev. D 49 (1994) 2642. ⇒37410.1103/PhysRevD.49.2642Search in Google Scholar

[22]C. M. Gonzalez, H. A Larrondo, O. A. Rosso,, Statistical complexity measure of pseudorandom bit generators Physica A 354 (2005) 281. ⇒37510.1016/j.physa.2005.02.054Search in Google Scholar

[23]A. Haar, Der Massbegri in der Theorie der kontinuierlichen Gruppen Ann. Math. 34 (1933) 147. ⇒38010.2307/1968346Search in Google Scholar

[24]J. Kogut, L. Susskind, Hamiltonian formulation of Wilson’s lattice gauge theories Phys. Rev. D 11 (1975) 395–408. ⇒38110.1103/PhysRevD.11.395Search in Google Scholar

[25]A. N. Kolmogorov, Entropy per unit time as a metric invariant of automorphism Doklady of Russian Academy of Sciences 124 (1959) 754–755. ⇒374Search in Google Scholar

[26]A-M. Kowalski, M-T. Martin, A. Plastino, O-A. Rosso, M. Casas, Distances in probability space and the statistical complexity setup Entropy 13 (2011) 1055–1075. ⇒37510.3390/e13061055Search in Google Scholar

[27]V. Kuvshinov, A. Kuzmin, Deterministic chaos in quantum field theory, Prog. Theor. Phys. Suppl. 150 (2003) 126–135. ⇒37410.1143/PTPS.150.126Search in Google Scholar

[28]P. T. Landsberg, J. S. Shiner, Disorder and complexity in an ideal non-equilibrium Fermi gas Phys. Lett. A 245 (1998) 228. ⇒392, 393, 39510.1016/S0375-9601(98)00361-2Search in Google Scholar

[29]A. Lempel, J. Ziv, On the complexity of finite sequences, IEEE Trans. Inform. Theory 22 (1976) 75–81. ⇒37410.1109/TIT.1976.1055501Search in Google Scholar

[30]G. Mack, Physical principles, geometrical aspects, and locality properties of gauge field theories, Fortsch. Phys. 29 (1981) 135. ⇒38110.1002/prop.19810290402Search in Google Scholar

[31]S. Mandelstam, Quantum electrodynamics without potentials Ann. Phys. 19 (1962) 1. ⇒38010.1016/0003-4916(62)90232-4Search in Google Scholar

[32]M. T. Martin, A. Plastino, O. A. Rosso, Statistical complexity and disequilibrium Phys. Lett A 311 (2003) 126. ⇒374, 392, 39310.1016/S0375-9601(03)00491-2Search in Google Scholar

[33]M. T. Martin, A. Plastino, O. A. Rosso, Generalized statistical complexity measures: Geometrical and analytical properties Physica A 369 (2006) 439–462. ⇒374, 39210.1016/j.physa.2005.11.053Search in Google Scholar

[34]I. Montvay, G. Münster, Quantum fields on a lattice, Cambridge University Press, Cambridge CB2 1RP, 1994. ⇒38010.1017/CBO9780511470783Search in Google Scholar

[35]B. Müller, A. Trayanov, Deterministic Chaos on Non-Abelian Lattice Gauge Theory, Phys. Rev. Letters 68 23 (1992) 3387–3390. ⇒374, 388, 39010.1103/PhysRevLett.68.338710045691Search in Google Scholar

[36]J. von Neumann, Thermodynamik quantenmechanischer Gesamtheiten, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen 1927 (1927) 273–291. ⇒375Search in Google Scholar

[37]L. E. Reichl, The Transition to Chaos, Springer-Verlag, 1992. ⇒38610.1007/978-1-4757-4352-4Search in Google Scholar

[38]A. Rényi, On measures of entropy and information. In Proc. of the 4th Berkeley Symposium on Mathematics, Statistics and Probability Neyman, J., Ed.; University of California Press: Berkeley, CA, USA, (1961) 547–561. ⇒374Search in Google Scholar

[39]M. Salicrú, M. L. Menéndez, D. Morales, L. Pardo, Asymptotic distribution of (h, ϕ)-entropies Commun. Stat. Theory Meth. 22 (1993) 2015–2031. ⇒37510.1080/03610929308831131Search in Google Scholar

[40]C. E. Shannon, A mathematical theory of communication Bell Syst. Tech. J. 27 (1948) 379–423. ⇒37410.1002/j.1538-7305.1948.tb01338.xSearch in Google Scholar

[41]J-S. Shiner, M. Davison, P-T. Landsberg, Phys. Rev. E 59, 2 (1999) 1459–1464. ⇒37410.1103/PhysRevE.59.1459Search in Google Scholar

[42]D. R. Stump, Entropy of the SU(2) lattice gauge field, Phys. Rev. D 36 (1987) 520. ⇒39110.1103/PhysRevD.36.5209958196Search in Google Scholar

[43]C. Tsallis, Possible generalization of Boltzmann–Gibbs statistics, J. Stat. Phys. 52 (1988) 479–487. ⇒37410.1007/BF01016429Search in Google Scholar

[44]S. Weinberg, The quantum theory of fields Cambridge Univ. Press 1996. ⇒38010.1017/CBO9781139644174Search in Google Scholar

[45]K. G. Wilson, Confinement of quarks, Phys. Rev. D 10 (1974)2445. ⇒38110.1103/PhysRevD.10.2445Search in Google Scholar

[46]W. K. Wootters, Statistical distance and Hilbert space, Phys. Rev. D 23 (1981)357. ⇒37410.1103/PhysRevD.23.357Search in Google Scholar

[47]C. N. Yang, Conservation of isotopic spin and isotopic gauge invariance, Phys. Rev. 96(1)(1954)191. ⇒37810.1103/PhysRev.96.191Search in Google Scholar