The chemical potentials of bosons and fermions is related to the number of particles and the temperature by Bose-Einstein statistics and Fermi-Dirac statistics respectively.
There are important differences between the statistical behavior of bosons and fermions, which are described by Bose-Einstein statistics and Fermi-Dirac statistics respectively.
Fermi-Dirac statistics / (1F:D)
Fermions are particles which satisfy Fermi-Dirac statistics.
Of interest to modern quantum optics, the different ytterbium isotopes follow either Bose-Einstein statistics or Fermi-Dirac statistics, leading to interesting behavior in optical lattices.
Fermi-Dirac statistics apply to fermions (particles that obey the Pauli exclusion principle), and Bose-Einstein statistics apply to bosons.
In Fermi-Dirac statistics (F-D statistics) interchanging any two particles of the system leaves the resultant system in an antisymmetric state.
Fermi-Dirac statistics is a theory that describes how collections of fermions behave.
Fermi-Dirac statistics is a part of the more general field of statistical mechanics and uses the principles of quantum mechanics.
Fermi-Dirac statistics continues to be an important part of physics.