The classical N-body problem within a generalized statistical mechanics

The modifications that must be introduced within the framework of standard, classical N-body statistical mechanics techniques, in order to deal with the recently proposed generalized scenario of non-extensive statistical mechanics are discussed. A generalized version of the equipartition theorem is shown to hold. The ideal gas is revisited as a simple application.

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

[2]  J. Lukierski,et al.  New quantum Poincaré algebra and κ-deformed field theory , 1992 .

[3]  C. Tsallis,et al.  Specific heat of the harmonic oscillator within generalized equilibrium statistics , 1989 .

[4]  C. Tsallis,et al.  Generalized statistical mechanics : connection with thermodynamics , 1991 .

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

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

[7]  R. Andrade Remarks on the behavior of the Ising chain in the generalized statistics , 1994 .

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

[9]  W. Fleming Functions of Several Variables , 1965 .

[10]  B. Zumino,et al.  A q-deformed Lorentz algebra , 1991 .

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

[12]  E. Jaynes Information Theory and Statistical Mechanics , 1957 .

[13]  AN INTRODUCTION TO NONCOMMUTATIVE DIFFERENTIAL GEOMETRY ON QUANTUM GROUPS , 1992, hep-th/9207084.

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

[15]  J. Lukierski,et al.  Q deformation of Poincare algebra , 1991 .

[16]  R. Balian From microphysics to macrophysics , 1991 .

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

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

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

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

[21]  C. Tsallis Possible generalization of Boltzmann-Gibbs statistics , 1988 .

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

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

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

[25]  C. Tsallis,et al.  Variational method in generalized statistical mechanics , 1993 .

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

[27]  L. Vinet,et al.  A note on (p, q)-oscillators and bibasic hypergeometric functions , 1993 .

[28]  B. Zumino,et al.  q-Deformed Poincaré algebra , 1992 .

[29]  I. Roditi,et al.  THERMO FIELD DYNAMICS OF DEFORMED SYSTEMS , 1993 .

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

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

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