this suggests that there is no limit in which the Bose-Einstein distribution for the photon becomes completely indistinguishable from the Boltzmann distribution. Even more strikingly, the distribution of diversity in a system obeying Fermi-Dirac statistics only approaches that of bosonic systems at extremely high temperatures, similar to those at the core of the sun.
As with the Boltzmann distributions, we find that the distributions of diversity for the two boson systems are independent of temperature.
Particularly, in the limit where q [right arrow] 1, the Tsallis distribution reduces to the standard Boltzmann distribution .
Particularly, if the Tsallis distribution describes the temperature fluctuations in wide transverse momentum spectrum which can be fitted by a two- or three-component Boltzmann distribution, the Tsallis forms of the standard distributions describe large temperature fluctuations in wider transverse momentum spectrum which can be fitted by a multicomponent Boltzmann distribution.
The standard Boltzmann distribution can be used to describe the particle behavior for single source.
process which results in a wider transverse momentum spectrum, the multicomponent Boltzmann distribution is needed.
Figure 3 shows the comparisons of different distributions with Boltzmann distribution on the same or similar transverse momentum spectrum.
We have [p.sub.T] distribution to be the Boltzmann distribution :
Then, we have a two-component revised Boltzmann distribution to be
The symbols represent the experimental data with different centralities measured by the PHENIX collaboration [38-40], and the curves are our results calculated by the two-component revised Boltzmann distribution. In the calculation, the values of the fitted parameters are obtained by fitting the experimental data and shown in Table 1 with values of [chi square]/dof ([chi] per degree of freedom).
The symbols represent the experimental data of the PHENIX collaboration  and the curves are our results calculated by the two-component revised Boltzmann distribution. We see again that the model describes well the experimental data.
In the above calculations, we have used the two-component revised Boltzmann distribution in which [p.sup.2.sub.T] exp(-[square root of [p.sup.2.sub.T] + [m.sup.2.sub.0]/T) is used to replace [p.sub.T] exp(-[square root of [p.sup.2.sub.T] + [m.sup.2.sub.0]]/T) T) in the original Boltzmann distribution.