# Integer Lattice Gas with Monte Carlo collision operator recovers the entropic lattice Boltzmann method with Poisson distributed fluctuations

## TL;DR

This paper introduces a Monte Carlo lattice gas model that mimics entropic lattice Boltzmann methods, providing insights into collision operators and fluctuations with Poisson statistics, advancing understanding of fluctuating lattice Boltzmann techniques.

## Contribution

It presents a novel Monte Carlo lattice gas model that recovers the entropic lattice Boltzmann method and elucidates the origin of multi-relaxation time collision operators and Poisson fluctuations.

## Key findings

- Derives equilibrium distribution for entropic lattice Boltzmann.
- Shows Galilean invariant fluctuations follow Poisson statistics.
- Provides insight into properties of fluctuating lattice Boltzmann methods.

## Abstract

We are examining a new kind of lattice gas that closely resembles modern lattice Boltzmann methods. This new kind of lattice gas, that we call a Monte Carlo Lattice Gas, has interesting properties that shed light on the origin of the multi-relaxation time collision operator and it derives the equilibrium distribution for entropic lattice Boltzmann. Furthermore these lattice gas methods have Galilean invariant fluctuations given by a Poisson statistics, giving further insight into the properties that we should expect for fluctuating lattice Boltzmann methods.