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Review of Tsallis distribution applied to RHIC data?

Review of Tsallis distribution applied to RHIC data?. NO! Theory about why is it applicable: yes!. T.S.Bíró, G.Purcsel and K.Ürmössy MTA KFKI RMKI Budapest. Talk given at Zimányi Winter School, 2008. nov. 25-29. Budapest, Hungary. Transverse momentum spectra.

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Review of Tsallis distribution applied to RHIC data?

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  1. Review of Tsallis distribution applied to RHIC data? NO! Theory about why is it applicable: yes! T.S.Bíró, G.Purcsel and K.Ürmössy MTA KFKI RMKI Budapest Talk given at Zimányi Winter School, 2008. nov. 25-29. Budapest, Hungary

  2. Transverse momentum spectra

  3. Transverse momentum spectra

  4. Transverse momentum spectra

  5. What all it can… • dN/dy rapidity distribution: reduced phase space (q < 1) • Multiplicity distribution: negative binomial • Temperature – average energy fluctuation • Superstatistics • Coalescence scaling for (q-1) Theory: thermodynamics with power-law tailed energy distributions

  6. Power-law tailed distributions and abstract composition rules T.S.Bíró, MTA KFKI RMKI Budapest Extensivity and non-extensivity Composition rules in the large-N limit Entropy formulas and distributions Relativistic kinetic energy composition Talk given at Zimanyi Winter School, 2008. nov. 25-29. Budapest, Hungary

  7. Extensivity andnon-extensivity T.S.Biro, arxiv:0809.4675 Europhysics Letters 2008 T.S.Biro, G.Purcsel, Phys.Lett.A 372, 1174, 2008 T.S.Biro, K.Urmossy, G.G.Barnafoldi, J.Phys.G 35:044012, 2008

  8. Extensive is not always additive

  9. Nonextensive as composite sums Pl. x_i=i, L(x)=exp(ax)

  10. Composition, large-N limit

  11. Composition, large-N limit

  12. Composition, large-N limit n = t N

  13. Composition by formal logarithm

  14. Asymptotic rules are associative

  15. Associative rules are asymptotic

  16. Associative rules areattractorsamong more general rules

  17. Entropy formulas, distributions

  18. Formal logarithm

  19. Deformed logarithm Deformed exponential

  20. Non-extensive entropy and energy

  21. Entropy maximum at fixed energy

  22. Canonical distribution and detailed balance solution in generalized Boltzmann equation:

  23. Example: Gibbs-Boltzmann

  24. Example: Tsallis

  25. Example: Kaniadakis

  26. Example: Einstein

  27. Example: Non associative

  28. Example: Non associative

  29. Generalized Boltzmann equation

  30. H theorem

  31. H theorem

  32. Relativistic energy composition

  33. Relativistic energy composition

  34. Angle averaged Q dependent composition rule for the relativistic kinetic energies

  35. Formal logarithm and asymptotic rule for the relativistic kinetic energies

  36. Asymptotic rule for m=0

  37. Summary • Non-extensive thermodynamics requires non-additive composition rules • Large N limit: rules are associative and symmetric, formal logarithm L • Entropy formulas, equilibrium distributions, H-theorem based on L • Relativistic kinematics  Tsallis-Pareto

  38. Appendix: how to throw new momenta?

  39. Appendix: how to throw new momenta?

  40. Appendix: how to throw new momenta for BG?

  41. Appendix: how to throw new momenta for Tsallis?

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