  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.
