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Non-extensive self-consistent thermodynamical theory
In experimental physics, researchers have proposed Non-extensive self-consistent thermodynamic theory to describe phenomena observed in the Large Hadron Collider (LHC). This theory investigates a fireball for high-energy particle collisions, while using Tsallis non-extensive thermodynamics. 〔 Fireballs lead to the bootstrap idea, or self-consistency principle, just as in the Boltzmann statistics used by Rolf Hagedorn.〔 Assuming the distribution function gets variations, due to possible symmetrical change, Abdel Nasser Tawfik applied the non-extensive concepts of high-energy particle production. 〔 〔
The motivation to use the non-extensive statistics from Tsallis() comes from the results obtained `by Bediaga et al.() They showed that with the substitution of the Boltzmann factor in Hagedorn's theory by the q-exponential function, it was possible to recover good agreement between calculation and experiment, even at energies as high as those achieved at the LHC, with q>1.
==Non-extensive entropy for ideal quantum gas==
The starting point of the theory is entropy for a non-extensive quantum gas of bosons and fermions, as proposed by Conroy, Miller and Plastino,〔 which is given by S_q=S_q^+S_q^ where S_q^ is the non-extended version of the Fermi–Dirac entropy and S_q^ is the non-extended version of the Bose–Einstein entropy.
That group 〔 and also Clemens and Worku, 〔 the entropy just defined leads to occupation number formulas that reduce to Bediaga's. C. Beck,〔 shows the power-like tails present in the distributions found in high energy physics experiments.
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