Nonextensivity: From Low-Dimensional Maps to Hamiltonian Systems

We present a brief pedagogical guided tour of the most recent applications of non-extensive statistical mechanics to well defined nonlinear dynamical systems, ranging from one-dimensional dissipative maps to many-body Hamiltonian systems.

[1]  A. Einstein,et al.  Theorie der Opaleszenz von homogenen Flüssigkeiten und Flüssigkeitsgemischen in der Nähe des kritischen Zustandes [AdP 33, 1275 (1910)] , 2005, Annalen der Physik.

[2]  S. Croucher,et al.  Surveys , 1965, Understanding Communication Research Methods.

[3]  Y. Pesin CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY , 1977 .

[4]  P. Landsberg,et al.  Thermodynamics and Statistical Mechanics , 1978 .

[5]  Nikolai SergeevichHG Krylov,et al.  Works on the foundations of statistical physics , 1979 .

[6]  H. Schuster Deterministic chaos: An introduction , 1984 .

[7]  Mw Hirsch,et al.  Chaos In Dynamical Systems , 2016 .

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

[9]  Ariel Fernández,et al.  H. G. Schuster: Deterministic Chaos, Second Revised Edition, VCH Verlagsgesellschaft, Weinheim. 273 Seiten, Preis: DM 108,– , 1988 .

[10]  Freddy Dumortier,et al.  Structures in Dynamics: Finite Dimensional Deterministic Studies , 1991 .

[11]  C. Beck,et al.  Thermodynamics of chaotic systems , 1993 .

[12]  C. Beck,et al.  Thermodynamics of chaotic systems : an introduction , 1993 .

[13]  J. Klafter,et al.  Lévy statistics in a Hamiltonian system. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[14]  S. Ruffo,et al.  Clustering and relaxation in Hamiltonian long-range dynamics. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[15]  Universal behavior of Lyapunov exponents in unstable systems. , 1995, Physical review letters.

[16]  Zanette,et al.  Thermodynamics of anomalous diffusion. , 1995, Physical review letters.

[17]  Per Bak,et al.  How Nature Works , 1996 .

[18]  C. Tsallis,et al.  Power-law sensitivity to initial conditions—New entropic representation , 1997 .

[19]  David M. Raup,et al.  How Nature Works: The Science of Self-Organized Criticality , 1997 .

[20]  A. Carbone,et al.  Constraints for solar neutrinos fluxes , 1997 .

[21]  Fractional kinetics and accelerator modes , 1997 .

[22]  D. Ion,et al.  ENTROPIC LOWER BOUND FOR THE QUANTUM SCATTERING OF SPINLESS PARTICLES , 1998 .

[23]  Vito Latora,et al.  Lyapunov Instability and Finite Size Effects in a System with Long-Range Forces , 1998 .

[24]  C. Tsallis,et al.  Breakdown of Exponential Sensitivity to Initial Conditions: Role of the Range of Interactions , 1998 .

[25]  C. Tsallis,et al.  Sensitivity to initial conditions in the Bak-Sneppen model of biological evolution , 1998 .

[26]  P. Landsberg,et al.  Distributions and channel capacities in generalized statistical mechanics , 1998 .

[27]  Anomalous diffusion as a signature of a collapsing phase in two-dimensional self-gravitating systems , 1998, cond-mat/9801008.

[28]  H. Posch,et al.  STATISTICAL MECHANICS AND COMPUTER SIMULATION OF SYSTEMS WITH ATTRACTIVE POSITIVE POWER-LAW POTENTIALS , 1998 .

[29]  E. Curado,et al.  A nonextensive thermodynamical equilibrium approach in e+e−→ hadrons , 1999, hep-ph/9905255.

[30]  D. Lynden-Bell NEGATIVE SPECIFIC HEAT IN ASTRONOMY, PHYSICS AND CHEMISTRY , 1999 .

[31]  V. Latora,et al.  Kolmogorov-Sinai Entropy Rate versus Physical Entropy , 1998, chao-dyn/9806006.

[32]  V. Latora,et al.  The rate of entropy increase at the edge of chaos , 1999, cond-mat/9907412.

[33]  Renio S. Mendes,et al.  Is re-association in folded proteins a case of nonextensivity? , 1999 .

[34]  SUPERDIFFUSION AND OUT-OF-EQUILIBRIUM CHAOTIC DYNAMICS WITH MANY DEGREES OF FREEDOMS , 1999, cond-mat/9904389.

[35]  A. Torcini,et al.  EQUILIBRIUM AND DYNAMICAL PROPERTIES OF TWO-DIMENSIONAL N-BODY SYSTEMS WITH LONG-RANGE ATTRACTIVE INTERACTIONS , 1999 .

[36]  Funabashi,et al.  Implications of Form Invariance to the Structure of Nonextensive Entropies , 1999, quant-ph/9904029.

[37]  Walton,et al.  Equilibrium distribution of heavy quarks in fokker-planck dynamics , 2000, Physical review letters.

[38]  Kudrolli,et al.  Non-gaussian velocity distributions in excited granular matter in the absence of clustering , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[39]  Marco Pettini,et al.  Geometric approach to Hamiltonian dynamics and statistical mechanics , 2000 .

[40]  Negative heat capacity in the critical region of nuclear fragmentation: an experimental evidence of the liquid-gas phase transition , 1999, nucl-ex/9906004.

[41]  Giorgio Parisi The physics of the glass transition , 2000 .

[42]  Microscopic dynamics of a phase transition: equilibrium vs out-of-equilibrium regime , 2000, nucl-th/0007038.

[43]  Canonical solution of a system of long-range interacting rotators on a lattice , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[44]  B. von Issendorff,et al.  Negative heat capacity for a cluster of 147 sodium atoms. , 2001, Physical review letters.

[45]  Pablo G. Debenedetti,et al.  Supercooled liquids and the glass transition , 2001, Nature.

[46]  H L Swinney,et al.  Measuring nonextensitivity parameters in a turbulent Couette-Taylor flow. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[47]  D. Gross,et al.  Microcanonical Thermodynamics: Phase Transitions in 'Small' Systems , 2001 .

[48]  Emergence of power-law correlation in 1-dimensional self-gravitating system , 2000, astro-ph/0008208.

[49]  Y. Sawada,et al.  Anomalous diffusion and non-Gaussian velocity distribution of Hydra cells in cellular aggregates , 2001 .

[50]  Marcelo A. Montemurro,et al.  Beyond the Zipf-Mandelbrot law in quantitative linguistics , 2001, ArXiv.

[51]  V Latora,et al.  Non-Gaussian equilibrium in a long-range Hamiltonian system. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[52]  V. Latora,et al.  Fingerprints of nonextensive thermodynamics in a long-range Hamiltonian system , 2002 .

[53]  The Hamiltonian Mean Field Model: From Dynamics to Statistical Mechanics and Back , 2002, cond-mat/0208456.

[54]  Negative specific heat in a Lennard-Jones-like gas with long-range interactions , 2001, cond-mat/0109504.

[55]  Philippe Chomaz,et al.  Phase Transitions in Finite Systems , 2002 .

[56]  A. Coniglio Clusters in frustrated systems , 2002 .

[57]  PDF of velocity fluctuation in turbulence by a statistics based on generalized entropy , 2001, cond-mat/0109007.

[58]  D. Gross,et al.  Thermo-statistics or Topology of the Microcanonical Entropy Surface , 2002 .