The Boltzmann equation evolves a phase-space distribution by balancing free streaming, external forces, and collisions.
Expanding an angular distribution in multipoles converts the Boltzmann equation into a hierarchy in which free streaming couples neighboring multipoles and collisions damp or source selected moments.
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The Boltzmann equation is a fundamental equation in statistical mechanics and kinetic theory that describes the statistical distribution of particles in a gas. It provides a framework for understanding how the microscopic properties of individual particles lead to macroscopic phenomena, such as temperature and pressure.