Abstract
Numerical solutions of the nonlinear Fokker-Planck equation (FPE) which has been associated with nonextensive q-statistics show that the available data on rapidity distributions for stopping in relativistic heavy-ion collisions cannot be reproduced with any permitted value of the nonextensivity parameter (1 < q < 1.5). This casts doubt on the nonextensivity concept that is widely used in relativistic heavy-ion physics.
Highlights
Nonextensive statistics proposes an extension of Boltzmann statistics through the concept of a non-additive q-entropy
It has been used in a nonlinear Fokker-Planck equation (FPE) for rapidity distributions, and applied to calculate rapidity and transverse momentum distributions for produced and stopped charged particles in relativistic heavy-ion collisions
We show that it is not possible to fit the data using solutions of the nonlinear FPE with values of the nonextensivity coefficient 1 < q < 1.5
Summary
Nonextensive statistics proposes an extension of Boltzmann statistics through the concept of a non-additive q-entropy. The measured charged-hadron rapidity distributions are found to be very broad compared to thermal model predictions [1], and the discrepancy increases strongly with energy This finding, as well as correspondingly broad net-proton (proton minus antiproton, or stopping) distributions [2, 3], indicates thermal diffusion plus collective expansion. With values of 1 < q < 1.5, the Fokker-Planck equation that has been used to model rapidity distributions [4] becomes nonlinear, it has an exponent (2 − q) in the diffusion term [6,7,8,9] This is supposed to account for long-range forces that cause collective expansion, and is considered to be a fundamental property of the system like the temperature T. They have been published in Ref. [13]
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