Thermodynamic properties at the kinetic freeze-out in the Au + Au and Cu + Cu collisions at the RHIC using the Tsallis distribution

The thermodynamic properties of charged particles,such as the energy density,pressure,entropy density,particle density,and squared speed of sound at the kinetic freeze-out in the Au+Au collisions from the relativistic heavy ion collider (RHIC)beam energy scan program √S_(NN) and in the Cu+Cu collisions at √S_(NN),200 GeV are studied using the thermodynamically consistent Tsallis distribution.The energy density,pressure,and particle density decrease monotonically with the collision energy for the same collision centrality;These properties also decrease monotonically from the central to peripheral collisions at the same collision energy.While the scaled energy densityε∕T^(4) and scaled entropy density s∕T^(3) demonstrate the opposite trend with the collision energy for the same collision centrality.There is a correlation betweenε∕T^(4) and s∕T^(3) at the same centrality.In addition,the squared speed of sound was calculated to determine that all the collision energies share nearly the same value at different collision centralities.

A new form of Tsallis distribution based on the probabilistically independent postulate

The current form of Tsallis distribution for a Hamiltonian system with an arbitrary potential is found to represent a simple isothermal situation. This paper finds that the q-exponential of a sum can be applied as the product of the q- exponential based on the probabilistically independent postulate employed in nonextensive statistical mechanics. Under this framework, a new form of Tsallis distribution is suggested. It shows that the new form of Tsallis distribution can supply the statistical description for the nonequilibrium dynamical property of the Hamiltonian system governed by an arbitrary potential, and it is found to be one potential statistical distribution for the dark matter.

Some dynamical property of the Tsallis distribution from a Fokker-Planck equation

This paper studies the possible dynamical property of the Tsallis distribution from a Fokker--Planck equation. For the Langevin dynamical system with an {arbitrary} potential function, Markovian friction and Gaussian white noise, it shows that the current form of Tsallis distribution cannot describe any nonequilibrium dynamics of the system, and it only stands for a simple isothermal situation of the system governed by a potential field. So the form of Tsallis distribution and many existing applications using the Tsallis distribution need to be reconsidered.

Energy and centrality dependence of light nuclei production in relativistic heavy-ion collisions

We study the energy and centrality dependence of deuteron and triton(helium-3)production in relativistic heavy-ion collisions at the BNL Relativistic Heavy Ion Collider(RHIC)and CERN Large Hadron Collider(LHC)using the Tsallis distribution,blast-wave(BW)model,and stationary Fokker-Planck(FP)solution.Our study shows that good agreement can be reached between the fitting results from the stationary FP solution and the experimental data for Au+Au collisions from the beam energy scan(BES)program of RHIC at√SNN=7.7,11.5,14.5,19.6,27,39,62.4,and 200 GeV and for Pb+Pb collisions at√SNN=2.76 TeV.The Tsallis distribution and BW model can reasonably describe the deuteron and triton(helium-3)trans verse momentum spectra obtained at RHIC and LHC.A more comprehensive comparison among the three methods suggests that the stationary FP solution is a sensible method,which is able to describe the energy dependence of the light nuclei yield ratio N_(t)N_(p)/N_(d)^(2) and provide a coherent description of deuteron and triton(helium-3)production for all centralities and various colliding energies at RHIC and LHC.