The partition function for "composite particles"

TL;DR

This paper derives explicit formulas for the partition function of composite particles in finite systems, providing insights into size corrections and thermodynamic limits for specific energy distributions.

Contribution

It introduces a method to transform the partition function into a finite sum for systems with uniform or linearly distributed energies, including finite size corrections.

Findings

Finite sum expressions for partition functions with uniform energy levels

Finite size corrections to the universal chiral partition function

Thermodynamic limit derivations for composite particles

Abstract

We calculate the partition function for "composite particles". For any finite number of states d, and in the following two cases: 1)all states have the same energy, 2)the energy is linearly distributed over the states, we transform the partition function into a finite sum of terms which exhibit trivially their $% d $dependance. The infinite d thermodynamic limit is obtained as well as the finite d-size corrections, etc. In the second case, we obtain the finite d-size corrections to "the universal chiral partition function for exclusion statistics".