Statistical Power-Law Spectra due to Reservoir Fluctuations

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 thermodynamical 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.