In
statistics the
Maxwell–Boltzmann distribution is a particular
probability distribution named after
James Clerk Maxwell and
Ludwig Boltzmann. It was first defined and used in
physics (in particular in
statistical mechanics) for describing particle speeds in idealized
gases where the particles move freely inside a stationary container without interacting with one another, except for very brief
collisions in which they exchange energy and momentum with each other or with their thermal environment. Particle in this context refers to gaseous particles (
atoms or
molecules), and the system of particles is assumed to have reached
thermodynamic equilibrium. While the distribution was first derived by Maxwell in 1860 on heuristic grounds, Boltzmann later carried out significant investigations into the physical origins of this distribution.