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

7. 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

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

9. Extensivity and non-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

10. Extensive is not always additive

11. Nonextensive is less tahn nonadditive

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

13. What is a problem? no problem: additive hence extensive problem: non-additive  belief: it becomes extensive in the large-N limit What to do if non-additive and non-extensive?

14. Example

15. Normalizations

16. Entropy: contribution of a pair

17. Entropy: N ptl-s N (N-1) / 2 pairs

18. Energy: N ptl-s N (N-1) / 2 pairs

19. Characteristic g(r) and … g(r) - g(r) ln g(r) g(r) v(r) weakly interacting pairs: Vinfo finite confined pairs: Vinfo may diverge

20. Large distance behavior

21. Composition, large-N limit

23. n = t N

24. Composition by formal logarithm

26. Asymptotic rules are associative

27. Associative rules are asymptotic

28. Associative rules are attractors among more general rules

29. Entropy formulas, distributions

30. Formal logarithm

31. Deformed logarithm Deformed exponential

32. Non-extensive entropy and energy

33. Entropy maximum at fixed energy

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

35. Example: Gibbs-Boltzmann

36. Example: Tsallis

37. Example: Kaniadakis

38. Example: Einstein

39. Example: Non associative

41. Generalized Boltzmann equation

42. H theorem

44. Relativistic energy composition

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

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

48. Asymptotic rule for m=0

49. 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

50. Appendix: how to throw new momenta?

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

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