Boltzmann equation is also known as Boltzmann transport equation (BTE) is used to study the statistical behaviour of the thermodynamic system which is not in a state of equilibrium. It was devised in the year 1872 by Ludwig Boltzmann.
Conservation equations: Boltzmann equation is used in the derivation of conservation laws of mass, momentum, charge and energy which are part of fluid dynamics.
Hamiltonian mechanics: Classical mechanics was reformulated as Hamiltonian mechanics with the help of different mathematical formulation.
Quantum theory and violation of particle number: Quantum Boltzmann equation is used to find out the number of particles that are not conserved in the collisions which is widely used in physical cosmology.
General relativity and astronomy: Boltzmann equation finds application in galactic dynamics.