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The effects of the non-extensive statistics on the nonlinear propagation of perturbations have been studied within the scope of relativistic second order dissipative hydrodynamics with the non-extensive equation of state. We have shown that the equations, describing the propagation of nonlinear waves under such situation are KdV-type (Korteweg-De Vries). Apart from their preserved solitonic behaviour the dissipative nature of these waves are also observed. The waves with larger amplitude and width dissipate less and propagate faster and these waves deplete more for both smaller values of Tsallis parameter ($q$) and temperature ($T$) of the medium. For vanishingly small transport coefficients the nonlinear waves show breaking nature. These findings suggest that the nature of the propagation of the nonlinear waves may serve as a good probe to differentiate between the extensive and non-extensive thermodynamic nature of a fluid, such as the quark-gluon plasma, produced in relativistic nuclear collisions., Comment: 28 pages (one LaTeX file for text and 7 figures)

The multiplicity, finite system size and collision energy dependencies of heat capacity ($C_V$), conformal symmetry breaking measure (CSBM) and speed of sound ($c_s$) have been investigated using ALICE data for $p+p$ collisions at $\sqrt{s}$ = 7 TeV. The aim of this study is to ascertain the possibility of formation of a thermalized medium in such collisions. We find that there is a threshold in charged particle multiplicity beyond which $C_V$, CSBM and $c_s$ attain plateau. The presence of such threshold in multiplicity is further reflected in the variation of these quantities with center-of-mass energy ($\sqrt{s_{NN}}$). In order to have a grasp on experimentally obtained results, variation of $\langle p_T \rangle$ with multiplicity has also been studied. The experimental results have been contrasted with PYTHIA8 and it is found that PYTHIA8 is inadequate to explain the features reflected in these quantities, thereby indicating the possibility of thermalization in such small system. It is also observed that the finite size effects alone cannot explain the non-extensive nature of particle spectra in $p+p$ collisions., Same as the published version

The high-multiplicity pp collisions at the Large Hadron Collider energies with various heavy-ion-like signatures have warranted a deeper understanding of the underlying physics and particle production mechanisms. It is a common practice to use experimental data on the hadronic transverse momentum ($p_T$) spectra to extract thermodynamical properties of the system formed in heavy ion and high multiplicity pp collisions. The non-availability of event topology dependent experimental data for pp collisions at $\sqrt{s}$ = 13 TeV on the spectra of non-strange and strange hadrons constrains us to use the PYTHIA8 simulated numbers to extract temperature-like parameters to study the event shape and multiplicity dependence of specific heat capacity, conformal symmetry breaking measure (CSBM) and speed of sound. The observables show a clear dependence on event multiplicity and event topology. Thermodynamics of the system is largely governed by the light particles because of their relatively larger abundances. In this regards, a threshold in the particle production, $\rm N_{ch} \simeq$ (10-20) in the final state multiplicity emerges out from the present study, confirming some of the earlier findings in this direction. As for heavier hadrons with relatively small abundances, a similar threshold is observed for $\langle \rm N_{ch} \rangle \simeq$ 40 hinting towards formation of a thermal bath where all the heavier hadrons are in equilibrium., Same as the published version

The hydrodynamic expansion rate of quark gluon plasma (QGP) is evaluated and compared with the scattering rate of quarks and gluons within the system. Partonic scattering rates evaluated within the ambit of perturbative Quantum Choromodynamics (pQCD) are found to be smaller than the expansion rate evaluated with ideal equation of state (EoS) for the QGP. This indicate that during the space-time evolution the system remains out of equilibrium. Enhancement of pQCD cross sections and a more realistic EoS keep the partons closer to the equilibrium., Comment: To be published in the Quark Matter 2008 poster proceedings

The medium modification of vector meson properties in hot/dense hadronic matter and its role in explaining the CERES/NA45 dilepton data at different centralities are discussed., Talk given at ICPA-QGP, Jaipur, November 2001