Boltzmann transport equation

The Boltzmann equation is a fundamental concept in physics used to describe the behavior of fluids, particularly gases, that are not in equilibrium. It's a complex mathematical tool that helps predict the motion of gas molecules.1

Developed from the kinetic theory of gases, the equation aims to explain macroscopic properties of gases by considering the statistical behavior and collisions of their constituent molecules. While the ideal gas model simplifies molecular interactions, the Boltzmann equation accounts for these collisions and external forces to describe how the distribution of molecular velocities changes over time. Solving the Boltzmann equation is challenging, but approximations allow scientists to understand deviations from equilibrium and calculate properties like viscosity and thermal conductivity. This work builds upon the foundations laid by physicist Ludwig Boltzmann, who pioneered statistical mechanics.234