Generalized statistical mechanics for superstatistical systems

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 369, Issue 1935, 2011, Pages 453-465

  Beck, Christian ^a  

^a QUEEN MARY UNIVERSITY OF LONDON   (United Kingdom)

Author keywords

Complex system; Fluctuating environment; Superstatistics

Indexed keywords

STATISTICAL MECHANICS;

COMPLEX SYSTEMS; ENERGY LEVEL; FLUCTUATING ENVIRONMENT; MESOSCOPIC SYSTEMS; SUPERSTATISTICS; TRAIN DELAY;

STATISTICS;

EID: 79251483166     PISSN: 1364503X     EISSN: None     Source Type: Journal    
DOI: 10.1098/rsta.2010.0280     Document Type: Article

References (51)

1. Beck, C. & Cohen, E. G. D. 2003 Superstatistics. Physica A 322, 267-275. (doi:10.1016/S0378-4371(03)00019-0)
2. Beck, C., Cohen, E. G. D. & Swinney, H. L. 2005 From time series to superstatistics. Phys. Rev. E 72, 056133. (doi:10.1103/PhysRevE.72.056133)
3. Touchette, H. & Beck, C. 2005 Asymptotics of superstatistics. Phys. Rev. E 71, 016131. (doi:10.1103/PhysRevE.71.016131)
4. Beck, C. & Cohen, E. G. D. 2004 Superstatistical generalization of the work fluctuation theorem. Physica A 344, 393-402. (doi:10.1016/j.physa.2004. 06.001)
5. Tsallis, C. & Souza, A. M. C. 2003 Constructing a statistical mechanics for Beck-Cohen superstatistics. Phys. Rev. E 67, 026106. (doi:10.1103/PhysRevE.67.026106)
6. Chavanis, P.-H. 2006 Coarse-grained distributions and superstatistics. Physica A 359, 177-212. (doi:10.1016/j.physa.2005.06.043)
7. Vignat, C., Plastino, A. & Plastino, A. R. 2005 Superstatistics based on the microcanonical ensemble. (http://arxiv.org/abs/cond-mat/0505580)
8. Vignat, C. & Plastino, A. 2007 Central limit theorem, deformed exponentials and superstatistics. (http://arxiv.org/abs/0706.0151)
9. Jizba, P. & Kleinert, H. 2008 Superpositions of probability distributions Phys. Rev. E 78, 031122. (doi:10.1103/PhysRevE.78.031122)
10. Wilk, G. & Wlodarczyk, Z. 2000 Interpretation of the nonextensive parameter q in some applications of Tsallis statistics and Levy distributions. Phys. Rev. Lett. 84, 2770-2773. (doi:10.1103/PhysRevLett.84.2770)
11. Beck, C. 2001 Dynamical foundations of nonextensive statistical mechanics. Phys. Rev. Lett. 87, 180601. (doi:10.1103/PhysRevLett.87.180601)
12. Frank, S. A. & Smith, D. E. 2010 Measurement invariance, entropy, and probability. Entropy 12, 289-303. (doi:10.3390/e12030289)
13. Hasegawa, Y. & Arita, M. 2010 Bistable stochastic processes in the q-exponential family. Physica A 389, 4450. (doi:10.1016/j.physa.2010.07.001)
14. Anteneodo, C. & Duarte Queiros, S. M. 2009 Statistical mixing and aggregation in Feller diffusion. J. Stat. Mech. P10023. (doi:10.1088/1742-5468/ 2009/10/P10023)
15. Abul-Magd, A. Y. 2009 Nonextensive and superstatistical generalizations of random-matrix theory. Eur. Phys. J. B 70, 39-48. (doi:10.1140/epjb/e2009- 00153-0)
16. Van der Straeten, E. & Beck, C. In press. Dynamical modelling of superstatistical complex systems. Physica A
17. Daniels, K. E., Beck, C. & Bodenschatz, E. 2004 Defect turbulence and generalized statistical mechanics. Physica D 193, 208-217. (doi:10.1016/j. physd.2004.01.033)
18. Baiesi, M., Paczuski, M. & Stella, A. L. 2006 Intensity thresholds and the statistics of the temporal occurence of solar flares. Phys. Rev. Lett. 96, 051103. (doi:10.1103/PhysRevLett.96.051103)
19. Reynolds, A. 2003 Superstatistical mechanics of tracer-particle motions in turbulence. Phys. Rev. Lett. 91, 084503. (doi:10.1103/PhysRevLett.91.084503)
20. Abul-Magd, A. Y. 2006 Superstatistics in random matrix theory. Physica A 361, 41-54. (doi:10.1016/j.physa.2005.07.019)
21. Abul-Magd, A. Y., Akemann, G. & Vivo, P. 2009 Superstatistical generalizations of Wishart-Laguerre ensembles of random matrices. J. Phys. A Math. Theor. 42, 175207. (doi:10.1088/1751-8113/42/17/175207)
22. Porporato, A., Vico, G. & Fay, P. A. 2006 Superstatistics of hydro-climatic fluctuations and interannual ecosystem productivity. Geophys. Res. Lett. 33, L15402. (doi:10.1029/2006GL026412)
23. Rizzo, S. & Rapisarda, A. 2004 Environmental atmospheric turbulence at Florence airport. AIP Conf. Proc. 742, 176-181. (doi:10.1063/1.1846475)
24. Laubrich, T., Ghasemi, F., Peinke, J. & Kantz, H. 2008 Statistical analysis of wind speed fluctuation and increments of non-stationary atmospheric boundary layer turbulence. (http://arxiv.org/abs/0811.3337)
25. Beck, C. 2004 Generalized statistical mechanics of cosmic rays. Physica A 331, 173. (doi:10.1016/j.physa.2003.09.025)
26. Ohtaki, Y. & Hasegawa, H. H. 2003 Superstatistics in econophysics. (http://arxiv.org/abs/cond-mat/0312568)
27. Van der Straeten, E. & Beck, C. 2009 Superstatistical fluctuations in time series: applications to share-price dynamics and turbulence. Phys. Rev. E 80, 036108. (doi:10.1103/PhysRevE.80.036108)
28. Aoyama, H., Yoshikawa, H., Iyetomi, H. & Fujiwara, Y. 2008 Productivity dispersion: facts,theory, and implications. (http://arxiv.org/abs/ 0805.2792)
29. Beck, C. 2007 Statistics of 3-dimensional Lagrangian turbulence. Phys. Rev. Lett. 98, 064502.
30. Beck, C. 2003 Lagrangian acceleration statistics in turbulent flows. Europhys. Lett. 64, 151. (doi:10.1209/epl/i2003-00498-4)
31. Wilk, G. & Wlodarczyk, Z. 2009 Power laws in elementary and heavy-ion collisions-a story of fluctuations and nonextensivity? Eur. Phys. J. A 40, 299-312. (doi:10.1140/epja/i2009-10803-9)
32. Beck, C. 2009 Superstatistics in high energy physics: application to cosmic ray energy spectra and e+e- annihilation. Eur. Phys. J. A 40, 267-273. (doi:10.1140/epja/i2009-10792-7)
33. Bouchard, J.-P. & Potters, M. 2003 Theory of financial risk and derivative pricing. Cambridge, UK: Cambridge University Press. (doi:10.1017/CBO9780511753893)
34. Ausloos, M. & Ivanova, K. 2003 Dynamical model and nonextensive statistical mechanics of a market index on large time windows. Phys. Rev. E 68, 046122. (doi:10.1103/PhysRevE.68.046122)
35. Abul-Magd, A. Y., Dietz, B., Friedrich, T. & Richer, A. 2008 Spectral fluctuations of billiards with mixed dynamics: from time series to superstatistics. Phys. Rev. E 77, 046202. (doi:10.1103/PhysRevE.77.046202)
36. Abe, S. & Thurner, S. 2005 Complex networks emerging from fluctuating random graphs: analytic formula for the hidden variable distribution. Phys. Rev. E 72, 036102. (doi:10.1103/PhysRevE.72.036102)
37. Duarte Queirós, S. M. 2008 On superstatistical multiplicative-noise processes. Braz. J. Phys. 38, 203. (doi:10.1590/S0103- 97332008000200001)
38. Briggs, K. & Beck, C. 2007 Modelling train delays with q-exponential functions. Physica A 378, 498-504. (doi:10.1016/j.physa.2006.11.084)
39. Leon Chen, L. & Beck, C. 2008 A superstatistical model of metastasis and cancer survival. Physica A 387, 3162. (doi:10.1016/j.physa.2008.01.116)
40. Abe, S., Beck, C. & Cohen, G. D. 2007 Superstatistics, thermodynamics, and fluctuations. Phys. Rev. E 76, 031102. (doi:10.1103/ PhysRevE.76.031102)
41. Crooks, G. E. 2007 Beyond Boltzmann-Gibbs statistics: maximum entropy hyperensembles out of equilibrium. Phys. Rev. E 75, 041119. (doi:10.1103/ PhysRevE.75.041119)
42. Naudts, J. 2007 Generalised thermostatistics using hyperensembles. AIP Conf. Proc. 965, 84-89. (doi:10.1063/1.2828764)
43. Van der Straeten, E. & Beck, C. 2008 Superstatistical distributions from a maximum entropy principle. Phys. Rev. E 78, 051101. (doi:10.1103/ PhysRevE.78.051101)
44. Tsallis, C. 1988 Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 52, 479. (doi:10.1007/BF01016429)
45. Mathai, A. M. & Haubold, H. J. 2007 Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy. Physica A 375, 110-122. (doi:10.1016/j.physa.2006.09.002)
46. Bianco, S., Grigolini, P. & Paradisi, P. 2005 Fluorescence intermittency in blinking quantum dots: renewal or slow modulation? (http://arxiv.org/abs/cond-mat/0509608)
47. Reynolds, A. M., Mordant, N., Crawford, A. M. & Bodenschatz, E. 2005 On the distribution of Lagrangian accelerations in turbulent flows. New J. Phys. 7, 58. (doi:10.1088/1367-2630/7/1/058)
48. Beck, C. 2000 Non-extensive statistical mechanics and particle spectra in elementary interactions. Physica A 286, 164-180. (doi:10.1016/S0378-4371(00) 00354-X)
49. Mavromatos, N. E. & Sarkar, S. 2009 Nonextensive statistics in stringy space-time foam models and entangled meson states. Phys. Rev. D 79, 104015. (doi:10.1103/PhysRevD.79.104015)
50. Beck, C. 2002 Spatio-temporal chaos and vacuum fluctuations of quantized fields. Singapore: World Scientific. (doi:10.1142/9789812778239)
51. Beck, C. 2002 Chaotic strings and standard model parameters. Physica D 171, 72-106. (doi:10.1016/S0167-2789(02)00540-7)