Hadron Multiplicity Distribution in Non Extensive Statistics Carlos E. Aguiar Takeshi Kodama UFRJ

Non Extensive Statistics Tsallis entropy: q-biased probabilities: Non extensivity: q-biased averages:

Tsallis Distribution Temperature: Variational principle: Probability distribution: “Partition function”:

Momentum Distribution NA22 250GeV/c

NA22 250GeV/c

NA22 250GeV/c

Multiplicity Distribution Deviation from Poisson

Multiplicity Distribution Deviation from Poisson

Multiplicity Distribution Deviation from Poisson

Multiplicity Distribution Deviation from Poisson

Multiplicity Distribution Deviation from Poisson

Multiplicity Distribution Deviation from Poisson

Negative-Binomial Distribution generating function: average and variance: k = - N binomial distribution k =  Poisson distribution

Multiplicity Distribution in Tsallis Statistics

Integral Representation for q > 1 maximum at x = 1, width = [q(q-1)] 1/2

Integral Representation of the Partition Function

Relativistic Ideal Gas No ideal Tsallis gas for q > 1 N particles:

Relativistic Van der Waals Gas W(x) = Lambert function: Number of particles < V / v v = “hard-core volume”

(q-1) << 1 and v/V << 1 First Order Corrections to Ideal Gas

Tsallis and Van der Waals Corrections Deviation from Poisson:

Tsallis - Van der Waals - Bose - Einstein Corrections Deviation from Poisson:

Multiple Fireballs  N fb k  N fb k N fb