# Multiple Exclusion Statistics

## TL;DR

This paper introduces a new distribution for particles obeying multiple exclusion, extending Haldane's statistics, and demonstrates its effectiveness through thermodynamic analysis and Monte Carlo simulations for lattice gases.

## Contribution

It proposes a novel multiple exclusion distribution based on an ansatz, generalizing Haldane's and Wu's distributions, with an exclusion spectrum function for correlated states.

## Key findings

- Excellent agreement with Monte Carlo simulations for k-mers from 2 to 10
- Generalizes existing exclusion statistics to correlated states
- Provides thermodynamic insights for lattice gases with multiple exclusion

## Abstract

A new distribution for systems of particles in equilibrium obeying exclusion of correlated states is presented following the Haldane's state counting. It relies upon an ansatz to deal with the multiple exclusion that takes place when the states accessible to single particles are spatially correlated and it can be simultaneously excluded by more than one particle. The Haldane's statistics and Wu's distribution are recovered in the limit of non-correlated states of the multiple exclusion statistics. In addition, an exclusion spectrum function $\mathcal{G}(n)$ is introduced to account for the dependence of the state exclusion on the occupation-number $n$. Results of thermodynamics and state occupation are shown for ideal lattice gases of linear particles of size $k$ ($k$-mers) where multiple exclusion occurs. Remarkable agreement is found with Grand-Canonical Monte Carlo simulations from $k$=2 to 10 where multiple exclusion dominates as $k$ increases.