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This study investigates city dynamics employing a nonextensive diffusion equation suited for addressing diffusion within a fractal medium, where the nonadditive parameter, $q$, plays a relevant role. The findings demonstrate the efficacy of this approach in determining the relation between the fractal dimension of the city, the allometric exponent and $q$, and elucidating the stationary phase of urban evolution. The dynamic methodology facilitates the correlation of the fractal dimension with both the entropic index and the urban scaling exponent identified in data analyses. The results reveal that the scaling behaviour observed in cities aligns with the fractal dimension measured through independent methods. Moreover, the interpretation of these findings underscores the intimate connection between the fractal dimension and social interactions within the urban context. This research contributes to a deeper comprehension of the intricate interplay between human behaviour, urban dynamics, and the underlying fractal nature of cities., Comment: 12 pages, 7 figures

Using the Plastino-Plastino (PP) equation, we calculate transport coefficients of the heavy-quarks traversing inside the quark-gluon plasma, and generalize their relationship with differential energy loss. The PP equation indicates anomalous diffusion of the probe particles and yields a quasi-exponential stationary distribution obtained also from the nonadditive statistics proposed by C. Tsallis. We estimate energy loss in a nonadditive quark-gluon medium, and calculate the jet-quenching parameter ($\hat{q}$) for the PP dynamics. With the help of the estimate of $\hat{q}$, we calculate the nuclear suppression factor ($R_{\text{AA}}$) of the heavy-quarks passing through a nonadditive quark-gluon plasma using the model proposed by Dokshitzer and Kharzeev. In many a case, the parameters in the analysis are fixed from the experimental results to minimize arbitrariness. There is a good agreement between the theoretical calculation and experimental $R_{\text{AA}}$ data, indicating that fast heavy-quarks may be subjected to anomalous diffusion inside the QGP., Comment: 12 pages, 4 figures

Particle production yields measured in central Au-Au collision at RHIC are obtained with free Fermi and Bose gases and also with a replacement of these statistics by non-extensive statistics. For the latter calculation, a set of different parameters was used with values of the Tsallis parameter $q$ chosen between 1.01 and 1.25, with 1.16 generating the best agreement with experimental data, an indication that non-extensive statistics may be one of the underlying features in heavy ion-collisions., Comment: 7 pages, 3 figures, 1 table

This study investigates the interconnections between the traditional Fokker-Planck Equation (FPE) and its fractal counterpart (FFPE), utilizing fractal derivatives. By examining the continuous approximation of fractal derivatives in the FPE, it derives the Plastino-Plastino Equation (PPE), which is commonly associated with Tsallis Statistics. This work deduces the connections between the entropic index and the geometric quantities related to the fractal dimension. Furthermore, it analyzes the implications of these relationships on the dynamics of systems in fractal spaces. In order to assess the effectiveness of both equations, numerical solutions are compared within the context of complex systems dynamics, specifically examining the behaviours of quark-gluon plasma (QGP). The FFPE provides an appropriate description of the dynamics of fractal systems by accounting for the fractal nature of the momentum space, exhibiting distinct behaviours compared to the traditional FPE due to the system's fractal nature. The findings indicate that the fractal equation and its continuous approximation yield similar results in studying dynamics, thereby allowing for interchangeability based on the specific problem at hand., Comment: 1 figure, 7 pages

This study focuses on the presence of (multi)fractal structures in confined hadronic matter through the momentum distributions of mesons produced in proton-proton collisions between 23 GeV and 63 GeV. The analysis demonstrates that the $q$-exponential behaviour of the particle momentum distributions is consistent with fractal characteristics, exhibiting fractal structures in confined hadronic matter with features similar to those observed in the deconfined quark-gluon plasma (QGP) regime. Furthermore, the systematic analysis of meson production in hadronic collisions at energies below 1 TeV suggests that specific fractal parameters are universal, independently of confinement or deconfinement, while others may be influenced by the quark content of the produced meson. These results pave the way for further research exploring the implications of fractal structures on various physical distributions and offer insights into the nature of the phase transition between confined and deconfined regimes., Comment: 23 pages, 11 figures, supplementary material

This work presents an analysis of fractional derivatives and fractal derivatives, discussing their differences and similarities. The fractal derivative is closely connected to Haussdorff's concepts of fractional dimension geometry. The paper distinguishes between the derivative of a function on a fractal domain and the derivative of a fractal function, where the image is a fractal space. Different continuous approximations for the fractal derivative are discussed, and it is shown that the $q$-calculus derivative is a continuous approximation of the fractal derivative of a fractal function. A similar version can be obtained for the derivative of a function on a fractal space. Caputo's derivative is also proportional to a continuous approximation of the fractal derivative, and the corresponding approximation of the derivative of a fractional function leads to a Caputo-like derivative. This work has implications for studies of fractional differential equations, anomalous diffusion, information and epidemic spread in fractal systems, and fractal geometry., Comment: 7 pages, 1 figure; v2 extended Discussion and Conclusions section, added Fig. 1 and references. Typos corrected. It matches the version published in MDPI Entropy

The Fokker-Planck Equation (FPE) is a fundamental tool for the investigation of kinematic aspects of a wide range of systems. For systems governed by the non-additive entropy $S_q$, the Plastino-Plastino Equation (PPE) is the correct generalization describing the kinematic evolution of such complex systems. Both equations have been applied for investigations in many fields, and in particular for the study of heavy quark evolution in the quark-gluon plasma. In the present work, we use this particular problem to compare the results obtained with the FPE and the PPE and discuss the different aspects of the dynamical evolution of the system according to the solutions for each equation. The comparison is done in two steps, first considering the modification that results from the use of a different partial derivative equation with the same transport coefficients, and then investigating the modifications by using the non-additive transport coefficients. We observe clear differences in the solutions for all the cases studied here and discuss possible experimental investigations that can indicate which of those equations better describes the heavy-quark kinematics in the medium. The results obtained here have implications in the study of anomalous diffusion in porous and granular media, in Cosmology and Astrophysics. The obtained results reinforce the validity of the relation $(q-1)^{-1}=(11/3)N_c-(4/3)(N_f/2)$, where $N_c$ and $N_f$ are, respectively, the number of colours and the effective number of flavours. This equation was recently established in the context of a fractal approach to QCD in the non-perturbative regime., Comment: 8 pages, 4 figures

In this work, we study the formal connections between the non-linear Fokker-Planck Equation associated with the non-additive entropy and the Boltzmann Equation with the non-additive correlation functional. The collisional term following the $q$-algebra is adopted. In the derivation of the non-additive Fokker-Planck Equation, two constraints are imposed on the final result: i) that the entropic index $q$ is a characteristic parameter of the non-additive systems with a value that does not change with time, and ii) that for $q \rightarrow 1$ a smooth transition for the standard Fokker-Planck Equation is obtained., Comment: 5 pages, no figures

We have studied the transverse momentum ($p_T$) spectra of the final-state strange particles, including $K^{\pm}$, $\phi$, $\it\Xi$, and $\it\Omega$, produced in high energy lead-lead (Pb-Pb), proton-lead ($p$-Pb), xenon-xenon (Xe-Xe) collisions at the Large Hadron Collider (LHC). Taking into account the contribution of multi-quark composition, whose probability density distribution is described by the modified Tsallis-Pareto-type function, we simulate the $p_T$ spectra of the final-state strange particles by a Monte Carlo method, which is shown to be in good agreement with the experimental data in most the cases. The kinetic freeze-out parameters are obtained. The present method provides a new tool for studying the spectra of various particles produced in high energy collisions, reflecting more realistically the collision process, which is of great significance to study the formation and properties of the produced particles., Comment: 19 pages, 9 figures. Advances in High Energy Physics, Accepted

The nonadditive entropy introduced by Tsallis in 1988 has been used in different fields and generalizes the Boltzmann entropy extending the possibilities of application of the statistical methods developed in the context of Mechanics. Here we investigate one of the last points of the theory that still are under discussion: the source term of the nonextensive transport equation. Based on a simple system, we show that the nonadditivity is a direct consequence of the phase space topology, and derive the source term that leads to the nonextensive transport equation., Comment: 8 pages

The Nambu--Jona-Lasino model is modified by the inclusion of a running-coupling that was obtained by a fractal approach to Quantum Chromodynamics. The coupling follows a $q$-exponential function and, in the context of high energy collisions, explains the origin of the Tsallis non-extensive statistics distributions. The parameter $q$ is completely determined in terms of the number of colours and the number of quark flavours. We study several aspects of the extended model and compare our results to the standard NJL model, where a constant coupling is used in combination with a sharp cutoff to regularize the gap equation. We show that the modified coupling regularizes the model like a smooth cutoff and reproduces the pion mass and decay constant, providing an almost exact Gell-Mann-Oakes-Renner relation at physical current quark masses., Comment: 14 pages, 6 figures, 1 table

The perturbative approach to QCD has been shown to be limited, and the difficulties to obtain accurate calculations in the low-energy region seems to be insurmountable. A recent approach uses the fractal structures of Yang-Mills Field Theory to circumvent those difficulties, allowing for the determination of an analytic expression for the running coupling. The results obtained are in agreement with several experimental findings, and explain many of the observed phenomena at high-energy collisions. In this work, we address some of the conceptual aspects of the fractal approach, which are expressed in terms of the renormalization group equation and the self-energy corrections to the parton mass. We associate these well-known concepts with the origins of the fractal structure in the quantum field theory., Comment: 8 pages, 1 figure, XLIV Brazilian Workshop on Nuclear Physics

We study the applications of non-extensive Tsallis statistics to high energy and hadron physics. These applications include studies of $pp$ collisions, equation of state of QCD, as well as Bose-Einstein condensation. We also analyze the connections of Tsallis statistics with thermofractals, and address some of the conceptual aspects of the fractal approach, which are expressed in terms of the renormalization group equation and the self-energy corrections to the parton mass. We associate these well-known concepts with the origins of the fractal structure in the quantum field theory., Comment: 16 pages, 8 figures. Talk given by E.Megias at the 10th International Conference on New Frontiers in Physics (ICNFP 2021), 23 Aug - 7 Oct 2021, Kolymbari, Crete, Greece

The interest in the Klein-Gordon equation with different potentials has increased in recent years due to its possible applications in Cosmology, Hadron Physics and High-Energy Physics. In this work we investigate the solutions of the Klein-Gordon equation for bosons under the influence of an external potential by using the Feshbach-Villars method. We present detailed results for two cases: the Coulombic potential and the harmonic potential. For the latter case, we studied the effects of self-interacting particles by adopting a mean-field approach. We show that our results converge smoothly to the solution of the Schr\"odinger equation for the same systems as the relativistic effects diminish., Comment: 8 pages, 3 figures; v2 typos corrected, added references, extended discussion. It matches the version published in The European Physical Journal Plus

The underlying connection between the degrees of freedom of a system and its nonextensive thermodynamic behavior is addressed. The problem is handled by starting from a thermodynamical system with fractal structure and its analytical reduction to a finite ideal gas. In the limit where the thermofractal has no internal structure, it is found that it reproduces the basic properties of a nonextensive ideal gas with a finite number of particles as recently discussed (Lima \& Deppman, Phys. Rev. E 101, 040102(R) 2020). In particular, the entropic $q$-index is calculated in terms of the number of particles both for the nonrelativistic and relativistic cases. In light of such results, the possible nonadditivity or additivity of the entropic structures are also critically analysed and new expressions to the entropy (per particle) for a composed system of thermofractals and its limiting case are derived., Comment: 6 pages, no figures

The neutrino-nucleus reactions are studied at energies from 0 to 3 GeV, using the CRISP program. To simulate these reactions, CRISP uses the Monte Carlo method through an intranuclear cascade model. Quase-elastic and baryonic resonance formation channels for the neutrino-nucleon interaction are considered. The total and differential particle emission cross-sections were obtained, obtaining a good agreement with the values reported by the MiniBooNE experiment. The influence of nuclear effects on the studied reactions, such as fermionic motion, the Pauli blocking mechanism, and the nucleonic separation energy, was shown. It was not possible to simultaneously reproduce the $\nu_\mu + D$ and $\nu_\mu + ^{12}C$ reactions using the same axial mass value. For the charged current quasi-elastic channel, $M_A = 0.95 \ GeV$ for the $\nu_\mu + D$ reaction, and $M_A = 1.35 \ GeV$ for the $\nu_\mu + ^{12}C$ reaction. This can be solved if one considers, in addition to the neutrino-nucleon interaction, the neutrino interaction with a pair of nucleons, just as we demonstrate in the last part of this work., Comment: 21 pages, 22 figures, 2 tables

Scale-free networks constitute a fast-developing field that has already provided us with important tools to understand natural and social phenomena. From biological systems to environmental modifications, from quantum fields to high energy collisions, or from the number of contacts one person has, on average, to the flux of vehicles in the streets of urban centres, all these complex, non-linear problems are better understood under the light of the scale-free network's properties. A few mechanisms have been found to explain the emergence of scale invariance in complex networks. Here we discuss a mechanism based on how information is locally spread among agents in a scale-free network. We show that the correct description of the information dynamics is given in terms of the q-exponential function, with the power-law behaviour arising in the asymptotic limit. This result shows that the best statistical approach to the information dynamics is given by Tsallis Statistics. We discuss the main properties of the information spreading process in the network and analyse the role and behaviour of some of the parameters as the number of agents increases. The different mechanisms for optimization of the information spread are discussed., Comment: 16 pages

We study the Bose-Einstein condensation in non-extensive statistics for a free gas of bosons, and extend the results to the non-relativistic case as well. We present results for the dependence of the critical temperature and the condensate fraction on the entropic index, q, and show that the condensate can exist only for a limited range of q in both relativistic and non-relativistic systems. We provide numerical results for other thermodynamics quantities like the internal energy, specific heat and number fluctuations. We discuss the implications for high energy physics and hadron physics. The results for the non-relativistic case can be of interest in cold-atom systems., Comment: 18 pages, 11 figures

We study the non-extensive Tsallis statistics and its applications to QCD and high energy physics, and analyze the possible connections of this statistics with a fractal structure of hadrons. Then, we describe how scaling properties of Yang-Mills theories allow the appearance of self-similar structures in gauge fields, which actually behave as fractals. The Tsallis entropic index, $q$, is deduced in terms of the field theory parameters, resulting in a good agreement with the value obtained experimentally., Comment: 6 pages, 4 figures. Talk given by E.Megias at the 23th International Conference in Quantum Chromodynamics (QCD 20), Montpellier, France, 27 - 30 October 2020. arXiv admin note: text overlap with arXiv:2002.12667

In this work, we provide an overview of the recent investigations on the non-extensive Tsallis statistics and its applications to high energy physics and astrophysics, including physics at the Large Hadron Collider (LHC), hadron physics, and neutron stars. We review some recent investigations on the power-law distributions arising in high energy physics experiments focusing on a thermodynamic description of the system formed, which~could explain the power-law behavior. The possible connections with a fractal structure of hadrons is also discussed. The main objective of the present work is to delineate the state-of-the-art of those studies and~show some open issues that deserve more careful investigation. We propose several possibilities to test the theory through analyses of experimental data., Comment: 27 pages, 10 figures; v2 typos corrected, added references. It matches the version published in MDPI Physics. arXiv admin note: text overlap with arXiv:2002.12667

Nonadditive Tsallis $q$-statistics has successfully been applied for a plethora of systems in natural sciences and other branches of knowledge. Nevertheless, its foundations have been severely criticised by some authors based on the standard additive Boltzmann-Gibbs approach thereby remaining a quite controversial subject. In order to clarify some polemical concepts, the distribution function for an ideal gas with a finite number of point particles and its $q$-index are analytically determined. The two-particle correlation function is also derived. The degree of correlation diminishes continuously with the growth of the number of particles. The ideal finite gas system is usually correlated, becomes less correlated when the number of particles grows, and is finally, fully uncorrelated when the molecular chaos regime is reached. It is also advocated that both approaches can be confronted through a careful kinetic spectroscopic experiment. The analytical results derived here suggest that Tsallis q-statistics may play a physical role more fundamental than usually discussed in the literature., Comment: 5 pages, no figures

The origin of non-extensive thermodynamics in physical systems has been under intense debate for the last decades. Recent results indicate a connection between non-extensive statistics and thermofractals. After reviewing this connection, we analyze how scaling properties of Yang-Mills theory allow the appearance of self-similar structures in gauge fields. The presence of such structures, which actually behave as fractals, allows for recurrent non-perturbative calculations of vertices. It is argued that when a statistical approach is used, the non-extensive statistics is obtained, and the Tsallis entropic index, $q$, is deduced in terms of the field theory parameters. The results are applied to QCD in the one-loop approximation, resulting in a good agreement with the value of $q$ obtained experimentally., Comment: 12 pages, 4 figures. Talk given by E.Megias at the 8th International Conference on New Frontiers in Physics (ICNFP 2019), 21-29 Aug 2019, Kolymbari, Crete, Greece

In this work we analyse how scaling properties of Yang-Mills field theory manifest as self-similarity of truncated n-point functions by scale evolution. The presence of such structures, which actually behaves as fractals, allow for recurrent non-perturbative calculation of any vertex. Some general properties are indeed independent of the perturbative order, what simplifies the non-perturbative calculations. We show that for sufficiently high perturbative orders a statistical approach can be used, the non extensive statistics is obtained, and the Tsallis index, $q$, is deduced in terms of the field theory parameters. The results are applied to QCD in the one-loop approximation, where $q$ can be calculated, resulting in a good agreement with the value obtained experimentally. We discuss how this approach allows to understand some intriguing experimental findings in high energy collisions, as the behavior of multiplicity against collision energy, long-tail distributions and the fractal dimension observed in intermittency analysis., Comment: 20 pages, 3 figures. arXiv admin note: text overlap with arXiv:1905.06382

In this work we present a bag-type model within a non-extensive statistics applied to the description of the properties of a hadronic system with an underlying fractal structure. The non-extensive ideal gas inside the bag is determined by the grand canonical partition function from which pressure, energy and particle density as well as temperature and chemical potential are obtained for the hadronic system. These quantities are studied in the approximation of fixed mass for all bag constituents but also for discrete and continuum masses. In all cases, the freeze-out line, corresponding to the energy per particle equal to 1 GeV and the lines corresponding to a fractal structure inside the proton volume are obtained. Finally, the pressure on the bag surface of the proton is calculated and the resulting value $(0.135\, {\rm GeV})^4$ obtained., Comment: 19 pages, 16 figures

The recent quantitative approaches for studing several aspects of urban life and infrastructure have shown that scale properties allow to understand many features of urban infrastructure and of human activity in cities. In this work, an analysis based on the complexity of cities network is performed for data on Brazilian cities firearms homicides. Due to the diversity in Brazilian population and cities, this is an interesting test for theories recently proposed. The superlinear power-law behavior for number of homicides as a function of city population, with exponent $\beta=1.15$ is obtained. The hypothesis that fractal structures can be formed in cities as well as in larger networks is tested, indicating that indeed self-similarity may be found in networks connecting several cities., Comment: 18 pages, 5 figures, 2 tables

Scaling properties of Yang-Mills fields are used to show that fractal structures are expected to be present in system described by those theories. We show that the fractal structure leads to recurrence formulas that allow the determination of non perturbative effective coupling. Fractal structures also cause the emergence of non extensivity in the system, which can be described by Tsallis statistics. The entropic index present in this statistics is obtained in terms of the field theory parameters. We apply the theory for QCD, and obtain the entropic index value, which is in good agreement with values obtained from experimental data. The Haussdorf dimension is calculated in terms of the entropic index, and the result for hadronic systems is in good agreement with the fractal dimension accessed by intermittency analysis of high energy collision data. The fractal dimension allow us to calculate the behavior of the particle multiplicity with the collision energy, showing again good agreement with data., Comment: 13 pages, 2 figures

The role played by non-extensive thermodynamics in physical systems has been under intense debate for the last decades. Some possible mechanisms that could give rise to non-extensive statistics have been formulated along the last few years, in particular the existence of a fractal structure in thermodynamic functions for hadronic systems. We investigate the properties of such fractal thermodynamical systems, in particular the fractal scale invariance is discussed in terms of the Callan-Symanzik~equation. Finally, we propose a diagrammatic method for calculations of relevant quantities., Comment: 5 pages, 2 figures. Presented by E.Megias at the QCD@Work: International Workshop on QCD, 25-28 June 2018, Matera, Italy

The role played by non extensive thermodynamics in physical systems has been under intense debate for the last decades. With many applications in several areas, the Tsallis statistics has been discussed in details in many works and triggered an interesting discussion on the most deep meaning of entropy and its role in complex systems. Some possible mechanisms that could give rise to non extensive statistics have been formulated along the last several years, in particular a fractal structure in thermodynamics functions was recently proposed as a possible origin for non extensive statistics in physical systems. In the present work we investigate the properties of such fractal thermodynamical system and propose a diagrammatic method for calculations of relevant quantities related to such system. It is shown that a system with the fractal structure described here presents temperature fluctuation following an Euler Gamma Function, in accordance with previous works that evidenced the connections between those fluctuations and Tsallis statistics. Finally, the fractal scale invariance is discussed in terms of the Callan-Symanzik Equation., Comment: 22 pages, 3 figures

The non extensive statistics proposed by C. Tsallis has found wide applicability, being present even in the description of experimental data from high energy collisions. A system with a fractal structure in its energy-momentum space, named thermofractal, was shown to be described thermodynamically by the non extensive statistics. Due to the many common features between thermofractals and Hagedorn's fireballs, this system offers the possibility to investigate the origins of non extensivity in hadronic physics and in QCD. In this regard, the investigation of the scaling properties of thermofractals through the renormalization group equation, known as Callan-Symanzik equation, can be an interesting approach., Comment: 6 pages. Accepted for publication in Adv. High Ener. Phys. 2018 (2018) 9141249

Nuclear reactions induced by muon neutrino with energies in the range from 0.2 to 1.5 GeV in Monte Carlo calculations framework in the intra-nuclear cascade model are studied. This study was done by comparison between the available experimental data and theoretical values of total cross section, and the energy distribution of emitted lepton energy in the reaction muon neutrino-nucleus, using the targets: $^{12}$C, $^{16}$O, $^{27}$Al, $^{40}$Ar, $^{56}$Fe and $^{208}$Pb. A phenomenological toy model of primary neutrino-nucleon interaction gives a good agreement of our theoretical inclusive neutrino nucleus cross in comparison with the available experimental data. Some interesting results on the behavior of the cross section as function of 1p-1n and higher contributions are also sketched. The previous results on the percentage of fake events related in available experiments in $^{12}$C were expanded for the set studied nuclei. With the increase of mass target, the nuclear effects in the cross sections were observed along with the importance to take into account fake events in the reactions.

In this work we revisit the MIT bag model to describe quark matter within both the usual Fermi-Dirac and the Tsallis statistics. We verify the effects of the non-additivity of the latter by analysing two different pictures: the first order phase transition of the QCD phase diagram and stellar matter properties. While, the QCD phase diagram is visually affected by the Tsallis statistics, the resulting effects on quark star macroscopic properties are barely noticed., Comment: 10 pagens, 5 figures

The non extensive aspects of $p_T$ distributions obtained in high energy collisions are discussed in relation to possible fractal structure in hadrons, in the sense of the thermofractal structure recently introduced. The evidences of self-similarity in both theoretical and experimental works in High Energy and in Hadron Physics are discussed, to show that the idea of fractal structure of hadrons and fireballs have being under discussion for decades. The non extensive self-consistent thermodynamics and the thermofractal structure allow one to connect non extensivity to intermittence and possibly to parton distribution functions in a single theoretical framework., Comment: 7 pages, ISMD2016 conference

In this work, we present new experimental data on mass distribution of fission fragments from $^{241}$Am proton-induced fission at $660$ MeV measured at the LNR Phasotron (JINR). The systematic analysis of several measured fragment mass distributions from different fission reactions available in the literature is also presented. The proton-induced fission of $^{241}$Am, $^{237}$Np and $^{238}$U at 26.5, 62.9 and 660 MeV was studied. The proton-induced fission of $^{232}$Th was studied at 26.5, 62.9 and 190 MeV. The fission of $^{208}$Pb also by a proton was investigated at 190, 500 and 1000 MeV. The fission of $^{197}$Au was studied for 190 and 800 MeV protons. Bremsstrahlung reactions with maximum photon energies of 50 and 3500 MeV were studied for $^{232}$Th and $^{238}$U. The framework of the Random Neck Rupture Model was applied in the analysis. The roles of the neutron excess and of the so called fissility parameter were also investigated.

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-H\"older 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., Comment: 22 pages

We present calculations for the incoherent photoproduction of J/$\psi$ vector mesons in ultra-peripheral heavy ion collisions (UPC) in terms of hadronic interactions. This study was carried out using the recently developed Monte Carlo model CRISP extended to include UPCs at LHC energies. A careful study of re-scattering and destruction of the J/$\psi$ particles is presented for PbPb collisions at $\sqrt{s_{NN}} = 2.76$ TeV. We have also compared our method to AuAu collisions at $\sqrt{s_{NN}} = 200$ GeV measured at RHIC., Comment: 6 pages, 7 figures

A systematic analysis of transverse momentum and rapidity distributions measured in high-energy proton - proton (pp) collisions for energies ranging from 53 GeV to 7 TeV using Tsallis thermodynamics is presented. The excellent description of all transverse momentum spectra obtained in earlier analyses is confirmed and extended. All energies can be described by a single Tsallis temperature of 68 +/- 5 MeV at all beam energies and particle types investigated (43 in total). The value of the entropic index, q, shows a wider spread but is always close to q approx 1.146. These values are then used to describe the rapidity distributions using a superposition of two Tsallis fireballs along the rapidity axis. It is concluded that the hadronic system created in high-energy p - p collisions between 53 GeV and 7 TeV can be seen as obeying Tsallis thermodynamics., Comment: 19 pages 22 figures