Fermi-Dirac statistics

Fermi-Dirac statistics describe the distribution of particles, specifically fermions (like electrons), that obey the Pauli exclusion principle, which states that no two fermions can occupy the same quantum state simultaneously. This principle explains why matter has structure; for example, why electrons fill up atomic orbitals in specific ways, impacting the properties of materials. Fermi-Dirac statistics apply at low temperatures and high densities, and are essential for understanding the behavior of systems such as metals, semiconductors, and even neutron stars, where fermionic particles govern their unique physical properties.