[Paper Review] How to observe fluctuating temperature?

O. V. Utyuzh, G. Wilk+1 more|ArXiv.org|Mar 26, 2001

Advanced Thermodynamics and Statistical Mechanics1 references3 citations

TL;DR

This paper proposes that event-by-event analysis of multiparticle production in heavy ion collisions can detect fluctuations in the temperature of the hadronizing source, using deviations from exponential $p_T$ spectra to reveal nonextensive statistics. It shows that fluctuating temperature within a single event leads to power-law (Lévy-type) distributions with $q > 1$, where $q-1$ corresponds to the inverse of the total heat capacity, offering a direct probe of thermodynamic properties and potential phase transitions.

ABSTRACT

We provide arguments that event-by-event (EBE) analysis of multiparticle production data are ideal place to search for the possible fluctuation of temperature characterizing hadronizing source in thermodynamical approach.

Motivation & Objective

• To investigate whether temperature fluctuations in high-energy multiparticle production can be observed experimentally.
• To distinguish between event-by-event temperature fluctuations and intra-event fluctuations as sources of non-exponential $p_T$ spectra.
• To establish a connection between the nonextensivity parameter $q$ and thermodynamic quantities like heat capacity.
• To provide a framework for detecting phase transitions via $q$-fluctuations in $p_T$ spectra.

Proposed method

• Use of event-by-event $p_T$ spectrum analysis to detect deviations from standard exponential distributions.
• Application of Tsallis statistics and Lévy distributions to model temperature fluctuations via the $q$-exponential form: $[1 + (1-q)\frac{\mu_T}{T_0}]^{1/(1-q)}$.
• Modeling temperature fluctuations via gamma-distributed inverse temperature $\beta = 1/T$, leading to $q = 1 + \omega$ with $\omega = \mathrm{var}(\beta)/\langle\beta\rangle^2$.
• Simulation of central Pb+Pb collisions at $E_{\text{beam}} = 3~A\cdot\text{TeV}$ with $dN/dy = 6000$ to compare exponential vs. power-law $p_T$ spectra.
• Derivation of the relation $C = 1/(q-1)$ linking the nonextensivity parameter $q$ to the total heat capacity $C$.

Experimental results

Research questions

• RQ1 Can fluctuations in the temperature of the hadronizing source be detected in $p_T$ spectra of high-energy collisions?
• RQ2 Is the observed deviation from exponential $p_T$ spectra due to event-by-event temperature variations or intra-event fluctuations?
• RQ3 Can the nonextensivity parameter $q$ in $q$-exponential distributions be interpreted as a measure of the system's heat capacity?
• RQ4 Does the $q$-parameter provide a direct probe of thermodynamic behavior, including possible phase transitions?

Key findings

• Intra-event temperature fluctuations lead to $p_T$ spectra described by a $q$-exponential (Lévy-type) distribution, deviating from standard exponential behavior.
• The parameter $q$ is related to the relative variance of $\beta = 1/T$ via $q = 1 + \omega$, where $\omega = \mathrm{var}(\beta)/\langle\beta\rangle^2$.
• The inverse of $q-1$ gives the total heat capacity $C = 1/(q-1)$, linking $q$ to thermodynamic stability and phase transitions.
• Simulations show that with $q = 1.05$, the $p_T$ spectrum bends upward at high momenta, indicating detectable deviation from exponential behavior.
• Event-by-event analysis is essential to distinguish between fluctuations from different initial conditions (inter-event) and intrinsic dynamical fluctuations (intra-event).