Thermodynamics with fractal structure, Tsallis statistics and hadrons

Abstract

A system presenting fractal structure in its thermodynamical functions is introduced, and it is shown that Tsallis statistics is the correct framework for describing the thermodynamical aspects of such fractal. Its Haussdorf dimension and its Lipshitz-Hölder exponent are determined in terms of the entropic index $q$. The connections with the intermittency in experimental data is discussed. The thermodynamical aspects of the thermofractal is related to the microscopic interaction of its components through the S-matrix.

22 pages

References in corpus (12)

• From QCD-based hard-scattering to nonextensive statistical mechanical descriptions of transverse momentum spectra in high-energy $pp$ and $p\bar{p}$ collisions
• Multiplicity fluctuations due to the temperature fluctuations in high-energy nuclear collisions
• Systematic analysis of pT -distributions in p + p collisions
• The Tsallis Distribution at Large Transverse Momenta
• Self-consistency in non-extensive thermodynamics of highly excited hadronic states
• Systematic analysis of hadron spectra in p+p collisions using Tsallis distribution
• Multifractal spectrum of phase space related to generalized thermostatistics
• Nonconcave entropies in multifractals and the thermodynamic formalism
• Fractality in momentum space: a signal of criticality in nuclear collisions
• Fission and spallation data evaluation using induced-activity method
• The world according to Renyi: Thermodynamics of multifractal systems
• Entropies from coarse-graining: convex polytopes vs. ellipsoids

Cited by in corpus (31)

• Fractals, non-extensive statistics and QCD
• Quark matter revisited with non extensive MIT bag model
• Fractal structure and non extensive statistics
• Investigating the inclusive transverse spectra in high-energy $pp$ collisions in the context of geometric scaling framework
• From the Boltzmann equation with non-local correlations to a standard non-linear Fokker-Planck equation
• Some intriguing aspects of multiparticle production processes
• Approach of complexity in nature: Entropic nonuniqueness
• Dynamics in fractal spaces
• Chemical freezeout parameters within generic nonextensive statistics
• Bag-type Model with Fractal Structure
• Lattice QCD thermodynamics and RHIC-BES particle production within generic nonextensive statistics
• Bose-Einstein condensation and non-extensive statistics
• QCD equation of state with Tsallis statistics for heavy-ion collisions
• Universal properties of primary and secondary cosmic ray energy spectra
• Thermodynamics from first principles: correlations and nonextensivity
• Fractal aspects of hadrons
• Role of chemical potential at kinetic freeze-out using Tsallis non-extensive statistics in proton-proton collisions at the Large Hadron Collider
• The Tsallis entropy and the BKT-like phase transition in the impact parameter space for $pp$ and $\bar{p}p$ collisions
• Transport Equation for Small Systems and Nonadditive Entropy
• Oscillations in multiparticle production processes
• Hollowness effect and entropy in high energy elastic scattering
• Scale dependence of the q and T parameters of the Tsallis distribution in the process of jet fragmentation
• Nonextensive percolation and Lee-Yang edge singularity from nonextensive $\lambda {\varphi }^3$ scalar field theory
• Non-extensive thermodynamics of the radiation in heterogeneous thermal plasmas
• Flux of information in scale-free networks
• QCD phase transition at finite temperature and chemical potential with the non-extensive statistics
• A Study of Multifractal Analysis in 16O-AgBr Collisions at 60A and 200A GeV
• Non-extensive Effects on the QCD Equation of State and Fluctuations of Conserved Charges within Polyakov Quark Meson Model
• Multiplicity dependence of strange and multi-strange hadrons in p$-$p, p$-$Pb and Pb$-$Pb collisions at LHC energies using Tsallis-Weibull Formalism
• Analytical calculations of the Quantum Tsallis thermodynamic variables
• Gauge fields renormalization groups and thermofractals