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The Boltzmann transport equation (BTE, also called the Boltzmann equation) is an equation describing the distribution of the velocity of particles in a gas, but is more general than the Maxwell-Boltzmann distribution because it does not presume equilibrium. It describes the distribution over time and converges with the Maxwell-Boltzmann distribution if equilibrium is reached, i.e., the gas has reached a state in which the distribution tends to remain the same. The equation has clear uses in astrophysics when an object such as a cloud or star lacks or loses its equilibrium, but has also been borrowed for use in the stellar dynamics of galaxies and stellar clusters, treating stars as its particles.
Note that another use of the term Boltzmann equation is for an equation modeling the distribution of atomic excitation levels in a gas.