Fermi–Dirac statistics

Summary

Fermi–Dirac statistics describes how identical fermions, such as electrons, fill the single-particle states of a system in thermal equilibrium. Because of the Pauli exclusion principle, each state holds at most one fermion, and the mean occupation of a state of energy $\varepsilon$ is $1/(e^{(\varepsilon - \mu)/k_B T} + 1)$. It explains the behaviour of electrons in metals, the stability of white dwarfs, and the small electronic heat capacity of solids. At high temperature or low density it reduces to Maxwell–Boltzmann statistics.