# Rigorous derivation of a ternary Boltzmann equation for a classical system of particles

## TL;DR

This paper rigorously derives a new kinetic equation for a classical particle system with three-particle interactions, advancing the modeling of non-ideal gases with higher-order interactions.

## Contribution

It introduces a novel ternary Boltzmann equation based on a non-symmetric ternary distance, extending kinetic theory to include three-particle elastic interactions.

## Key findings

- Derivation of a new ternary Boltzmann equation.
- First step towards modeling non-ideal gases with higher-order interactions.
- Provides a mathematical framework for three-particle elastic collisions.

## Abstract

In this paper, we present a rigorous derivation of a new kinetic equation describing the limiting behavior of a classical system of particles with three particle elastic instantaneous interactions, which are modeled using a non-symmetric version of a ternary distance. The ternary collisional operator we derive can be seen as the first step towards obtaining a toy model for a non-ideal gas where higher order interactions are taken into account.