Finite heat reservoir capacity and temperature fluctuations lead to modification of the well known canonical exponential weight factor. Requiring that the corrections least depend on the one-particle energy, we derive a deformed entropy, K(S). The re
sulting formula contains the Boltzmann-Gibbs, the Renyi and the Tsallis formulas as particular cases. For extreme large fluctuations (compared to the Gaussian case) a new, parameter-free entropy - probability relation emerges. This formula and the corresponding canonical equilibrium distribution are nearly Boltzmannian for high probability, but deviate from the classical result for low probability. In the extreme large fluctuation limit the canonical distribution resembles for low probability the cumulative Gompertz distribution.
LHC ALICE data are interpreted in terms of statistical power-law tailed pT spectra. As explanation we derive such statistical distributions for particular particle number fluctuation patterns in a finite heat bath exactly, and for general thermodynam
ical systems in the subleading canonical expansion approximately. Our general result, $q = 1 - 1/C + Delta T^2 / T^2$, demonstrates how the heat capacity and the temperature fluctuation effects compete, and cancel only in the standard Gaussian approximation.
This article presents the basic idea of VHMPID, an upgrade detector for the ALICE experiment at LHC, CERN. The main goal of this detector is to extend the particle identification capabilities of ALICE to give more insight into the evolution of the ho
t and dense matter created in Pb-Pb collisions. Starting from the physics motivations and working principles the challenges and current status of development is detailed.
