Statistical Power-Law Spectra due to Reservoir Fluctuations

TL;DR

This paper derives statistical power-law spectra from particle number fluctuations in finite systems, explaining LHC ALICE data through thermodynamic effects like heat capacity and temperature fluctuations.

Contribution

It provides an exact derivation of power-law spectra from fluctuation patterns and introduces a general formula linking heat capacity and temperature fluctuations.

Findings

Power-law spectra arise from particle number fluctuations.

Heat capacity and temperature fluctuations influence spectral shapes.

Standard Gaussian approximation cancels fluctuation effects.

Abstract

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.