Equivalence of volume and temperature fluctuations in power-law ensembles

TL;DR

This paper demonstrates the equivalence of volume and temperature fluctuations in power-law ensembles under constant energy, linking Tsallis statistics to volume fluctuations and exploring their implications for high-energy particle collision data analysis.

Contribution

It shows that volume fluctuations are equivalent to temperature fluctuations in power-law ensembles and introduces methods to distinguish event-level from event-to-event fluctuations.

Findings

Volume fluctuations are equivalent to temperature fluctuations at fixed energy.

Fluctuations induce specific correlations among particles.

Proposes a method to differentiate fluctuation types in high-energy collisions.

Abstract

Relativistic particle production often requires the use of Tsallis statistics to account for the apparently power-like behavior of transverse momenta observed in the data even at a few GeV/c. In such an approach this behavior is attributed to some specific intrinsic fluctuations of the temperature $T$ in the hadronizing system and is fully accounted by the nonextensivity parameter $q$. On the other hand, it was recently shown that similar power-law spectra can also be obtained by introducing some specific volume fluctuations, apparently without invoking the introduction of Tsallis statistics. We demonstrate that, in fact, when the total energy is kept constant, these volume fluctuations are equivalent to temperature fluctuations and can be derived from them. In addition, we show that fluctuations leading to multiparticle power-law Tsallis distributions introduce specific correlations between the considered particles. We then propose a possible way to distinguish the fluctuations in each event from those occurring from event-to-event. This could have applications in the analysis of high density events at LHC (and especially in ALICE).