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An analytical formula that accurately accounts for the Lorentz contraction ofthe excluded volume of two relativistic hadrons with hard-core repulsion isworked out. Using the obtained expression we heuristically derive the equationof state of Boltzmann particles with relativistic excluded volumes in terms ofsystem pressure and its surface and curvature tension coefficients. Thebehavior of effective excluded volumes of lightest baryons and mesons isstudied at very high temperatures (particle number densities) and for verylarge values of degeneracy factors. Several parameterizations of the obtainedequation of state demonstrate a universal asymptotics of the effective excludedvolume at high particle number densities. It is peculiar, that the foundmaximal packing fraction $\eta \simeq 0.75$ of Lorentz contracted particles isvery close to the dense packing limit of classical hard spheres of same radius$\eta_{exc} \approx 0.74$. We show that the developed equation of state is thegrand canonical formulation of the morphological thermodynamics approachapplied to Lorentz contracted rigid spheres.

physica scripta

Induced Surface and Curvature Tensions Equation of State of Hadrons with  Relativistic Excluded Volumes and its Relation to Morphological  Thermodynamics