A system of quantum statistics that is used to describe the behaviour of solids in terms of a free electron model. In this model the most weakly bound electrons of the constituent atoms are considered to behave as a gas subject to certain conditions: the electrons are free to move in any direction through the solid, they do not interact with each other, and are subject to the Pauli exclusion principle.
The probability of an energy level of energy E being occupied by an electron is given by the Fermi–Dirac distribution function, f(E):
where EF is the Fermi level, k is the Boltzmann constant, and T the thermodynamic temperature.
The free electron model is used to explain a number of important physical properties of metals.