Maxwell–Boltzmann statistics

Summary

Maxwell–Boltzmann statistics describes how non-interacting classical particles share out among the energy levels of a system in thermal equilibrium. Let $T$ be the temperature and $k_B$ the Boltzmann constant. The mean number of particles in a level of energy $\varepsilon$ is proportional to $e^{-\varepsilon / k_B T}$. It is the classical counterpart of Fermi–Dirac statistics and Bose–Einstein statistics, and both reduce to it when the occupation of every state is small. Applied to the kinetic energy of a gas, it gives the Maxwell–Boltzmann distribution of molecular speeds.