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

TL;DR

This paper derives an analytical equation of state for relativistic hadrons with Lorentz-contracted excluded volumes, linking it to morphological thermodynamics and revealing universal high-density behavior.

Contribution

It introduces a novel analytical formula accounting for Lorentz contraction in hadron excluded volumes and connects it to morphological thermodynamics.

Findings

Maximal packing fraction close to dense packing limit of spheres

Universal asymptotics of effective excluded volume at high densities

Equation of state applicable to high-temperature hadronic matter

Abstract

An analytical formula that accurately accounts for the Lorentz contraction of the excluded volume of two relativistic hadrons with hard-core repulsion is worked out. Using the obtained expression we heuristically derive the equation of state of Boltzmann particles with relativistic excluded volumes in terms of system pressure and its surface and curvature tension coefficients. The behavior of effective excluded volumes of lightest baryons and mesons is studied at very high temperatures (particle number densities) and for very large values of degeneracy factors. Several parameterizations of the obtained equation of state demonstrate a universal asymptotics of the effective excluded volume at high particle number densities. It is peculiar, that the found maximal packing fraction $\eta \simeq 0.75$ of Lorentz contracted particles is very 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 the grand canonical formulation of the morphological thermodynamics approach applied to Lorentz contracted rigid spheres.