Nonextensive physics: a possible connection between generalized statistical mechanics and quantum groups

Abstract Two different formalisms have been recently developed for nonextensive physics, namely the generalized statistical mechanics and thermodynamics (characterized by q ≠1) and the quantum groups (characterized by q G ≠1). Through the discussion of the mean values of observables, we propose a (temperature dependent) connection between q and q G , and illustrate with bosonic oscillators.

[1]  H. Bacry.  The existence of dark matter in question , 1993 .

[2]  P. T. Landsberg,et al.  Is equilibrium always an entropy maximum? , 1984 .

[3]  L. Nottale.  Fractal space-time and microphysics , 1993 .

[4]  R. Mishra,et al.  Self-Organization , 2021, Encyclopedic Dictionary of Archaeology.

[5]  E. Athanassoula,et al.  N-body problems and gravitational dynamics , 1993 .

[6]  Ott,et al.  Anomalous diffusion in "living polymers": A genuine Levy flight? , 1990, Physical review letters.

[7]  E. Witten.  Gauge theories, vertex models, and quantum groups , 1990 .

[8]  C. Tsallis,et al.  Specific heat of a free particle in a generalized Boltzmann-Gibbs statistics , 1993 .

[9]  D. Stariolo.  The Langevin and Fokker-Planck equations in the framework of a generalized statistical mechanics , 1994 .

[10]  A. Plastino.  Dynamical aspects of Tsallis' entropy , 1994 .

[11]  E. Montroll,et al.  Maximum entropy formalism, fractals, scaling phenomena, and 1/f noise: A tale of tails , 1983 .

[12]  C. Tsallis,et al.  Generalized simulated annealing , 1995, cond-mat/9501047.

[13]  E. Mello,et al.  The fluctuation-dissipation theorem in the framework of the Tsallis statistics , 1994 .

[14]  Lucena,et al.  Departure from Boltzmann-Gibbs statistics makes the hydrogen-atom specific heat a computable quantity. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  Anyonic realization of SUq(N) quantum algebra , 1993, hep-th/9302111.

[16]  A. Mariz,et al.  On the irreversible nature of the Tsallis and Renyi entropies , 1992 .

[17]  Jeffrey M. Hausdorff,et al.  Long-range anticorrelations and non-Gaussian behavior of the heartbeat. , 1993, Physical review letters.

[18]  Anyons and quantum groups , 1993, hep-th/9301100.

[19]  Constantino Tsallis,et al.  The classical N-body problem within a generalized statistical mechanics , 1994 .

[20]  D. Ellinas,et al.  Quantum algebra as the dynamical symmetry of the deformed Jaynes-Cummings model. , 1990, Physical review letters.

[21]  M. Chaichian,et al.  Quantum lie superalgebras and q-oscillators , 1990 .

[22]  A. R. Plastino,et al.  Tsallis' entropy, Ehrenfest theorem and information theory , 1993 .

[23]  John D. Ramshaw.  H-theorems for the Tsallis and Renyi Entropies , 1993 .

[24]  A. R. Plastino,et al.  Stellar polytropes and Tsallis' entropy , 1993 .

[25]  Mixing and "violent relaxation" for the one-dimensional gravitational Coulomb gas. , 1989, Physical review. A, General physics.

[26]  W. Saslaw,et al.  Gravitational Physics of Stellar and Galactic Systems: Finite spherical systems – clusters of galaxies, galactic nuclei, globular clusters , 1985 .

[27]  Fevzi Büyükkiliç,et al.  A fractal approach to entropy and distribution functions , 1993 .

[28]  A. Dimakis,et al.  Quantum mechanics on a lattice and q-deformations , 1992 .

[29]  John D. Ramshaw.  Irreversibility and generalized entropies , 1993 .

[30]  Irreversible thermodynamics in the framework of Tsallis entropy , 1995 .