Generalised information and entropy measures in physics

References

• Beck , C. and Schlögl , F. 1993 . Thermodynamics of Chaotic Systems , Cambridge, , UK : Camdridge University Press .
   Google Scholar
• Tsallis , C. 1988 . Possible generalization of Boltzmann–Gibbs statistics . J. Stat. Phys. , 52 : 479 – 487 .
   Web of Science ®Google Scholar
• Tsallis , C. , Mendes , R. S. and Plastino , A. R. 1998 . The role of constraints within generalized nonextensive statistics . Physica A , 261 : 534 – 554 .
   Web of Science ®Google Scholar
• Kaniadakis , G. 2002 . Statistical mechanics in the context of special relativity . Phys. Rev. E , 66 : 056125
   Web of Science ®Google Scholar
• Naudts , J. 2004 . Generalized thermostatistics based on deformed exponential and logarithmic functions . Physica A , 340 : 32 – 40 .
   Web of Science ®Google Scholar
• Abe , S. , Beck , C. and Cohen , E. G.D. 2007 . Superstatistics, thermodynamics, and fluctuations . Phys. Rev. E , 76 : 031102
   Web of Science ®Google Scholar
• Chavanis , P.-H. 2008 . Nonlinear mean field Fokker–Planck equations. Application to the chemotaxis of biological populations . Eur. Phys. J. B , 62 : 179 – 208 .
   Web of Science ®Google Scholar
• Beck , C. 2004 . Generalized statistical machanics of cosmic rays . Physica A , 331 : 173 – 181 .
   Web of Science ®Google Scholar
• Daniels , K. E. , Beck , C. and Bodenschatz , E. 2004 . Defect turbulence and generalized statistical machanics . Physica D , 193 : 208 – 217 .
   Web of Science ®Google Scholar
• Lutz , E. 2003 . Anomalous diffusion and Tsallis statistics in an optical lattice . Phys. Rev. A , 67 : 051402
   Web of Science ®Google Scholar
• Douglas , P. , Bergamini , S. and Renzoni , F. 2006 . Tunable Tsallis distributions in dissipative optical lattices . Phys. Rev. Lett. , 96 : 110601
   PubMed Web of Science ®Google Scholar
• Beck , C. and Cohen , E. G.D. 2003 . Superstatistics . Physica A , 322 : 267 – 275 .
   Web of Science ®Google Scholar
• Beck , C. , Cohen , E. G.D. and Swinney , H. L. 2005 . From time series to superstatistics . Phys. Rev. E , 72 : 056133
   Web of Science ®Google Scholar
• Reynolds , A. 2003 . Superstatistical mechanics of tracer- particle motions in turbulence . Phys. Rev. Lett. , 91 : 084503
   PubMed Web of Science ®Google Scholar
• Beck , C. 2007 . Statistics of three-dimensional Lagrangian turbulence . Phys. Rev. Lett. , 98 : 064502
   PubMed Web of Science ®Google Scholar
• Bediaga , I. , Curado , E. M.F. and de Miranda , J. M. 2000 . A nonextensive thermodynamic equilibrium approach in e + e − → hadrons . Physica A , 286 : 156 – 163 .
   Web of Science ®Google Scholar
• Beck , C. 2000 . Non-extensive statistical mechanics and particle spectra in elementary interactions . Physica A , 286 : 164 – 180 .
   Web of Science ®Google Scholar
• Plastino , A. R. and Plastino , A. 1993 . Stellar polytropes and Tsallis' entropy . Phys. Lett. A , 174 : 384 – 386 .
   Web of Science ®Google Scholar
• Chavanis , P.-H. 2003 . Generalized thermodynamics and Fokker–Planck equations: Applications to stellar dynamics and two-dimensional turbulence . Phys. Rev. E , 68 : 036108
   Web of Science ®Google Scholar
• Pluchino , A. , Latora , V. and Rapisarda , A. 2004 . Glassy dynamics in the HMF model . Physica A , 340 : 187 – 195 .
   Web of Science ®Google Scholar
• Pluchino , A. , Rapisarda , A. and Tsallis , C. 2007 . Nonergodicity and central-limit behavior for long-range Hamiltonians . Europhys. Lett. , 80 : 26002
   Google Scholar
• Borland , L. 2002 . Option pricing formulas based on a non-Gaussian stock price model . Phys. Rev. Lett. , 89 : 098701
   PubMed Web of Science ®Google Scholar
• Upadhyaya , A. , Rieu , J.-P. , Glazier , J. A. and Sawada , Y. 2001 . Anomalous diffusion and non-Gaussian velocity distribution of Hydra cells in cellular aggregates . Physica A , 293 : 549 – 558 .
   Web of Science ®Google Scholar
• Chen , L. L. and Beck , C. 2008 . A superstatistical model of metastasis and cancer survival . Physica A , 387 : 3162 – 3172 .
   Web of Science ®Google Scholar
• Khinchin , A. I. 1957 . Mathematical Foundations of Information Theory Dover, New York
   Google Scholar
• Rényi , A. 1970 . Probability Theory North Holland, Amsterdam
   Google Scholar
• Havrada , J. H. and Charvat , F. 1967 . Quantification methods of classification processes: Concepts of structural α entropy . Kybernetica , 3 : 30 – 35 .
   Google Scholar
• Tsallis , C. , Gell-Mann , M. and Sato , Y. 2005 . Asymptotically scale-invariant occupancy of phase space makes the entropy S q extensive . Proc. Nat. Acad. Sci. , 102 : 15377 – 15382 .
   PubMed Web of Science ®Google Scholar
• Landsberg , P. T. and Vedral , V. 1998 . Distributions and channel capacities in generalized statistical mechanics . Phys. Lett. A , 247 : 211 – 217 .
   Web of Science ®Google Scholar
• Abe , S. 1997 . A note on the q-deformation-theoretic aspect of the generalized entropies in nonextensive physics . Phys. Lett. A , 224 : 326 – 330 .
   Web of Science ®Google Scholar
• Sharma , B. D. and Mittal , D. P. 1975 . New nonadditive measures of entropy for discrete probability distributions . J. Math. Sci. , 10 : 28 – 40 .
   Google Scholar
• Abe , S. 2000 . Axioms and uniqueness theorem for Tsallis entropy . Phys. Lett. A , 271 : 74 – 79 .
   Web of Science ®Google Scholar
• Wada , T. and Suyari , H. A two-parameter generalization of Shannon–Khinchin axioms and the uniqueness theorem, preprint (2006). Available at cond-mat/0608139 .
   Google Scholar
• Lesche , B. 1982 . Instabilities of Rényi entropies . J. Stat. Phys. , 27 : 419 – 422 .
   Web of Science ®Google Scholar
• Abe , S. 2002 . Stability of Tsallis entropy and instabilities of Rényi and normalized Tsallis entropies: A basis for q-exponential distributions . Phys. Rev. E , 66 : 046134
   Web of Science ®Google Scholar
• Hanel , R. , Thurner , S. and Tsallis , C. 2009 . On the robustness of q-expectation values and Rényi entropy . Europhys. Lett. , 85 : 20005
   Google Scholar
• Jaynes , E. T. 1957 . Information theory and statistical mechanics . Phys. Rev. , 106 : 620 – 630 .
   Web of Science ®Google Scholar
• Hagedorn , R. 1965 . Statistical thermodynamics of strong interactions at high energies . Nuovo Cim. Suppl. , 3 : 147 – 186 .
   Google Scholar
• Wilk , G. and Wlodarczyk , Z. 2000 . Interpretation of the nonextensive parameter q in some applications of Tsallis statistics and Lévy distributions . Phys. Rev. Lett. , 84 : 2770 – 2773 .
   PubMed Web of Science ®Google Scholar
• Beck , C. 2001 . Dynamical foundations of nonextensive statistical mechanics . Phys. Rev. Lett. , 87 : 180601
   Web of Science ®Google Scholar
• Van der Straeten , E. and Beck , C. 2008 . Superstatistical distributions from a maximum entropy principle . Phys. Rev. E , 78 : 051101
   Web of Science ®Google Scholar
• Tsallis , C. and Souza , A. M.C. 2003 . Constructing a statistical mechanics for Beck–Cohen superstatistics . Phys. Rev. E , 67 : 026106
   Web of Science ®Google Scholar
• Bouchard , J.-P. and Potters , M. 2003 . Theory of Financial Risk and Derivative Pricing , Cambridge, , UK : Cambridge University Press .
   Google Scholar
• Briggs , K. and Beck , C. 2007 . Modelling train delays with q-exponential functions . Physica A , 378 : 498 – 504 .
   Web of Science ®Google Scholar