Induced surface and curvature tension equation of state for hadron resonance gas in finite volumes and its relation to morphological thermodynamics

TL;DR

This paper develops a novel equation of state for hadron resonance gases in finite volumes, incorporating surface and curvature tensions, and applies it to analyze particle production and freeze-out conditions in high-energy nuclear collisions.

Contribution

It introduces an original approach to derive surface and curvature tension equations of state for finite hadron systems, extending morphological thermodynamics to this context.

Findings

Metastable states appear at high pressures in finite systems.

The developed equations are applicable to small volumes above 20 fm$^3$.

The model successfully describes particle ratios in heavy-ion collisions.

Abstract

Here we develop an original approach to investigate the grand canonical partition function of the multicomponent mixtures of Boltzmann particles with hard-core interaction in finite and even small systems of the volumes above 20 fm$^3$. The derived expressions of the induced surface tension equation of state are analyzed in details. It is shown that the metastable states, which can emerge in the finite systems with realistic interaction, appear at very high pressures at which the hadron resonance gas, most probably, is not applicable at all. It is shown how and under what conditions the obtained results for finite systems can be generalized to include into a formalism the equation for curvature tension. The applicability range of the obtained equations of induced surface and curvature tensions for finite systems is discussed and their close relations to the equations of the morphological thermodynamics are established. The hadron resonance gas model on the basis of the obtained advanced equation of state is worked out. Also, this model is applied to analyze the chemical freeze-out of hadrons and light nuclei with the number of (anti-)baryons not exceeding 4, including the most problematic ratios of hyper-triton and its antiparticle. Their multiplicities were measured by the ALICE Collaboration in the central lead-lead collisions at the center-of-mass energy $\sqrt{s_{\rm NN}} =$ 2.76 TeV.