Fermi–Dirac statistics

Fermi–Dirac statistics gives the probability that a quantum state is occupied by indistinguishable fermions in thermal equilibrium. Each state can contain at most one fermion of a given spin state, reflecting the Pauli exclusion principle.

Fermi–Dirac distribution: The mean occupation of a single-particle energy state by fermions at a specified temperature and chemical potential. This formula expresses the statistics as an energy-dependent occupation probability.
Fermion: A particle with half-integer spin that obeys Fermi–Dirac statistics and the Pauli exclusion principle. Fermions are the particles whose allowed occupations the statistics describes.
Electron gas: A collection of mobile electrons modeled as particles moving through a material or space. Its occupied energy states are commonly calculated using Fermi–Dirac statistics.
Bose–Einstein statistics: The quantum statistics governing indistinguishable bosons, which can share a quantum state without an occupation limit. Bosons may accumulate in one state, unlike fermions governed by exclusion.
Pauli exclusion principle: No two identical fermions can occupy the same quantum state simultaneously. Exclusion limits each state’s occupation and produces the characteristic distribution.
Quantum state: A mathematical description containing the information available about a quantum system. The distribution assigns an occupation to each available single-particle state.
Fermi gas: An idealized system of noninteracting fermions obeying the Pauli exclusion principle. It is the standard model for applying the distribution to many-particle systems.
Maxwell–Boltzmann statistics: Classical statistics describing particle populations when quantum effects and indistinguishability are negligible. It approximates fermion occupations when states are sparsely populated and quantum degeneracy is weak.
Chemical potential: The change in a system’s free energy when one particle is added, at fixed temperature and volume. It sets the energy around which occupation changes from likely to unlikely.
Indistinguishable particles: Quantum particles that cannot be individually distinguished by any physical measurement. Indistinguishability is essential to the quantum statistics of identical fermions.

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