Maxwell-Boltzmann Distribution

The Maxwell-Boltzmann distribution gives the range of speeds a gas's molecules actually have at a given temperature, rather than treating them as moving uniformly: most molecules cluster around a typical speed, with a long tail moving faster or slower, and the distribution's shape shifts predictably as temperature rises. James Clerk Maxwell formulated the underlying kinetic theory around 1866, independently of Ludwig Boltzmann, who derived the distribution rigorously in 1871 and generalized the statistical treatment considerably further over the following decades; the result is credited to both names jointly rather than to either alone.