Equivalence of the phenomenological Tsallis distribution to the transverse momentum distribution of $q$-dual statistics

Abstract

In the present work, we have found that the phenomenological Tsallis distribution (which nowadays is largely used to describe the transverse momentum distributions of hadrons measured in $pp$ collisions at high energies) is consistent with the basis of the statistical mechanics if it belongs to the $q$-dual nonextensive statistics instead of the Tsallis one. We have defined the $q$-dual statistics based on the $q$-dual entropy which was obtained from the Tsallis entropy under the multiplicative transformation of the entropic parameter $q\to 1/q$. We have found that the phenomenological Tsallis distribution is equivalent to the transverse momentum distribution of the $q$-dual statistics in the zeroth term approximation. Since the $q$-dual statistics is properly defined, it provides a correct link between the phenomenological Tsallis distribution and the second law of thermodynamics.

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• Multi-source thermal model describing multi-region structure of transverse momentum spectra of identified particles and parameter dynamics of system evolution in relativistic collisions
• Comparing effective temperatures in standard, Tsallis, and q-dual statistics from transverse momentum spectra of identified light charged hadrons produced in gold--gold collisions at RHIC energies
• Analyzing the Correlation Between Thermal and Kinematic Parameters in Various Multiplicity Classes within 7 and 13 TeV pp Collisions
• Extracting Kinetic Freeze-out Properties in High Energy Collisions Using a Multi-source Thermal Model
• Thermodynamic relations and fluctuations in the Tsallis statistics
• Analytical Results for the Classical and Quantum Tsallis Hadron Transverse Momentum Spectra: the Zeroth Order Approximation and beyond
• On Extracting Thermal Parameters and Scenario in High-Energy Collisions
• Comparing effective temperatures in standard and Tsallis distributions from transverse momentum spectra in small collision systems
• Gauge fields renormalization groups and thermofractals
• Study of invariance of nonextensive statistics under the uniform energy spectrum translation
• Analytical calculations of the Quantum Tsallis thermodynamic variables