Fermi–Dirac statistics | DisamKB

Fermi–Dirac statistics

E4993

quantum statistics statistical distribution

Fermi–Dirac statistics is the quantum statistical framework that describes the distribution and behavior of indistinguishable fermions, such as electrons, which obey the Pauli exclusion principle.

Aliases (1)

Fermi–Dirac distribution ×5

Statements (49)

Predicate	Object
instanceOf	quantum statistics → statistical distribution →
appliesTo	electrons → fermions → neutrinos → neutrons → particles with half-integer spin → protons → quarks →
assumes	indistinguishability of particles → quantum mechanical description of states →
basedOnPrinciple	Pauli exclusion principle →
contrastsWith	Bose–Einstein statistics → Maxwell–Boltzmann statistics →
describes	degenerate Fermi gas → equilibrium distribution of indistinguishable fermions → occupation number distribution of fermions →
domain	quantum mechanics → thermodynamics →
formulatedBy	Enrico Fermi → Paul Dirac →
hasDistributionFunction	f(E) = 1 / (exp((E − μ) / kT) + 1) →
hasParameter	Boltzmann constant k → chemical potential μ → temperature T →
historicalDevelopment	formulated in the 1920s →
implies	maximum of one fermion per single-particle quantum state →
mathematicalFramework	grand canonical ensemble →
namedAfter	Enrico Fermi → Paul Dirac →
reducesTo	Maxwell–Boltzmann statistics at high temperature and low density →
relatedConcept	Fermi energy → Fermi gas → Fermi level → degenerate matter →
usedIn	astrophysics → condensed matter physics → metallic conduction theory → neutron star models → nuclear physics → quantum many-body theory → semiconductor physics → solid-state physics → statistical mechanics → white dwarf star models →
usedToExplain	degeneracy pressure in neutron stars → degeneracy pressure in white dwarfs → electron distribution in metals → electronic heat capacity of metals →

Referenced by (15)

Subject (surface form when different)	Predicate
Boltzmann distribution ("Fermi–Dirac distribution") → Bose–Einstein statistics → Maxwell–Boltzmann statistics →	contrastsWith
Fermi energy → Pauli exclusion principle ("Fermi–Dirac distribution") →	relatedTo
Boltzmann constant ("Fermi–Dirac distribution") →	appearsIn
k_B ("Fermi–Dirac distribution") →	appearsInEquation
Chandrasekhar limit →	basedOn
Pauli exclusion principle →	hasConsequence
Fermi gas ("Fermi–Dirac distribution") →	hasDistributionFunction
Enrico Fermi →	knownFor
Enrico Fermi →	notableFor
Fermi gas →	obeys
muon neutrino →	obeysStatistics
tau lepton →	statistics