# From creation and annihilation operators to statistics

## TL;DR

This paper presents a method to derive the partition function for particles with exotic statistics using creation and annihilation operators, covering various types including ewkons, which may model dark energy.

## Contribution

It introduces a direct procedure linking partition functions to specific operator relations for exotic statistics, expanding understanding of non-standard quantum gases.

## Key findings

- Derived partition functions for Gentile, quons, Polychronakos, and ewkons statistics.
- Ewkons exhibit negative pressure, relevant for dark energy modeling.
- Method connects operator algebra to thermodynamic properties of exotic particles.

## Abstract

A procedure to derive the partition function of non-interacting particles with exotic or intermediate statistics is presented. The partition function is directly related to the associated creation and annihilation operators that obey some specific commutation or anti-commutation relations. The cases of Gentile statistics, quons, Polychronakos statistics, and ewkons are considered. Ewkons statistics was recently derived from the assumption of free diffusion in energy space (Phys. Rev. E 94, 062115, 2016); an ideal gas of ewkons has negative pressure, a feature that makes them suitable for the description of dark energy.