The Boltzmann equation forms the basis of kinetic theory, which provides the bridge between microscopic and macroscopic physics. This equation belongs to the realm of statistical mechanics, and it describes the motion of large numbers of particles in a statistical sense. The Boltzmann equation allows for a systematic derivation of macroscopic transport processes like diffusion, heat flow and conductivity from the underlying microscopic laws of nature. Though it applies only to dilute systems, it underlies theories that are of tremendous practical and technological importance, such as fluid, aero- and plasma dynamics. This equation forms the solid basis for the description of systems that are not in equilibrium, in particular for analyzing processes that lead to equilibrium.

To describe the behavior of macroscopic systems like gases or liquids, one does not need to know the detailed properties of all the individual particles making up the gas or liquid. Fortunately, because that would involve solving a system of 1023 or more coupled equations. It suffices to know the average properties of particles, and that is where statistical considerations come in. Now the fact that we have to deal with very many particles becomes a blessing in disguise: as every casino owner or insurance company can tell you, statistical arguments become extremely accurate and thus powerful if one is dealing with large numbers. So, whereas the motion of the individual particles in a fluid or gas may be quite random, the statistical distribution function describing the probabilities of where they are and what velocity they have is not, and it is this distribution function which has to satisfy some fundamental equation. In a gas, for example, evidently not all molecules sit together in one place: they spread more or less evenly through the available space, and one also expects that because of the collisions of the molecules, the energy will be more or less equally distributed among the molecules once the system is in equilibrium. The importance of the Boltzmann equation is that it also describes processes that deviate from the equilibrium; for example, it allows one to prove that a process leads to equilibrium.