# Viscosity calculations from Hadron Resonance Gas model: Finite size effect

## TL;DR

This paper investigates how finite system size affects shear and bulk viscosities in the hadron resonance gas model, proposing a size-dependent upper bound that refines previous estimates and suggests hadronic matter may be nearly perfect fluid.

## Contribution

It introduces a phenomenological finite size correction to transport coefficients in the HRG model, applicable to other models, and refines the range of estimated viscosities.

## Key findings

- Finite size reduces thermodynamical phase space for particles.
- Finite size limits relaxation times of hadrons.
- Proposed upper bounds narrow the viscosity estimates.

## Abstract

We have attempted to review on microscopic calculation of transport coefficients like shear and bulk viscosities in the framework of hadron resonance gas model, where a special attention is explored on the effect of finite system size. The standard expressions of transport coefficients, obtained from relaxation time approximation of kinetic theory or diagrammatic Kubo-type formalism, carry mainly two temperature dependent components -- thermodynamical phase space and relaxation time of medium constituent. Owing to quantum effect of finite system size, thermodynamical phase space can be reduced as its momentum distribution will be started from some finite lower momentum cut-off instead of zero momentum. On the other hand, relaxation time of hadrons can also face finite size effect by considering only those relaxation scales, which are lower than the system size. Owing to these phenomenological issues, we have proposed a system size dependent upper bound of transport coefficients for ideal HRG model, whose qualitative technique may also be applicable in other models. This finite size prescription may guide to shorten the broad numerical band, within which earlier estimated values of transport coefficients for hadronic matter are located. It is also suspected that the hadronic matter may not be far from the (nearly) perfect fluid nature like the quark gluon plasma.