Relativistic transformation of thermodynamic parameters and refined Saha equation

The relativistic transformation rule for temperature is a debated topic for more than 110 years.Several incompatible proposals exist in the literature but a final resolution is still missing.In this work,we reconsider the problem of relativistic transformation rules for a number of thermodynamic parameters including temperature,chemical potential,pressure,entropy and enthalpy densities for a relativistic perfect fluid using relativistic kinetic theory.The analysis is carried out in a fully relativistic covariant manner,and the explicit transformation rules for the above quantities are obtained in both Minkowski and Rindler spacetimes.Our results suggest that the temperature of a moving fluid appears to be colder,supporting the proposal by de Broglie,Einstein,and Planck,in contrast to other proposals.Moreover,in the case of a Rindler fluid,our findings suggest that the total number of particles and the total entropy of a perfect fluid in a box whose bottom is parallel to the Rindler horizon are proportional to the area of the bottom,but are independent of the height of the box,provided the bottom of the box is sufficiently close to the Rindler horizon.The area dependence of the particle number implies that the particles tend to be gathered toward the bottom of the box,and hence implicitly determines the distribution of the chemical potential of the system,whereas the area dependence of the entropy indicates that the entropy is still additive and may have potential applications in explaining the area law of black hole entropy.As a by-product,we also obtain a relativistically refined version of the famous Saha equation which holds in both Minkowski and Rindler spacetimes.

Relativistic gravitational collapse by thermal mass

Gravity and thermal energy are universal phenomena which compete over the stabilization of astrophysical systems.The former induces an inward pressure driving collapse and the latter a stabilizing outward pressure generated by random motion and energy dispersion.Since a contracting self-gravitating system is heated up one may wonder why is gravitational collapse not halted in all cases at a sufficient high temperature establishing either a gravo-thermal equilibrium or explosion.Here,based on the equivalence between mass and energy,we show that there always exists a temperature threshold beyond which the gravitation of thermal energy overcomes its stabilizing pressure and the system collapses under the weight of its own heat.

On thermodynamic self-consistency of generic axiomatic-nonextensive statistics

Generic axiomatic-nonextensive statistics introduces two asymptotic properties,to each of which a scaling function is assigned.The first and second scaling properties are characterized by the exponents c and d,respectively.In the thermodynamic limit,a grand-canonical ensemble can be formulated.The thermodynamic properties of a relativistic ideal gas of hadron resonances are studied,analytically.It is found that this generic statistics satisfies the requirements of the equilibrium thermodynamics.Essential aspects of the thermodynamic self-consistency are clarified.Analytical expressions are proposed for the statistical fits of various transverse momentum distributions measured in most-central collisions at different collision energies and colliding systems.Estimations for the freezeout temperature（T_（ch）） and the baryon chemical potential（μ_b） and the exponents c and d are determined.The earlier are found compatible with the parameters deduced from Boltzmann-Gibbs（BG） statistics（extensive）,while the latter refer to generic nonextensivities.The resulting equivalence class（c,d） is associated with stretched exponentials,where Lambert function reaches its asymptotic stability.In some measurements,the resulting nonextensive entropy is linearly composed on extensive entropies.Apart from power-scaling,the particle ratios and yields are excellent quantities to highlighting whether the particle production takes place（non）extensively.Various particle ratios and yields measured by the STAR experiment in central collisions at 200,62.4 and 7.7 GeV are fitted with this novel approach.We found that both c and d 〈 1,i.e.referring to neither BG-nor Tsallis-type statistics,but to（c,d）-entropy,where Lambert functions exponentially rise.The freezeout temperature and baryon chemical potential are found comparable with the ones deduced from BG statistics（extensive）.We conclude that the particle production at STAR energies is likely a nonextensive process but not necessarily BG or Tsallis type.