The Boltzmann equation is a fundamental equation in statistical mechanics that describes the behavior of a gas in equilibrium, taking into account the interactions between individual particles. It provides a way to study the distribution of particles in a gas as they move and collide with each other. The equation was first formulated by the Austrian physicist Ludwig Boltzmann in the late 19th century and has since been used in a wide range of fields, including physics, chemistry, and engineering. Researchers use the Boltzmann equation to understand the behavior of gases, plasmas, and other complex systems, and to develop models and simulations to predict their properties and behavior.