Phase-space distribution function ($f(\mathbf{x},\mathbf{p})$)

A phase-space distribution function gives the occupation density of particles as a function of position and momentum. For a spatially homogeneous gas it depends only on momentum.

The number density is the number of particles per unit volume. For a homogeneous species with $g$ internal states and phase-space distribution $f(\mathbf{p})$ in natural units,

Column density is the number density integrated along a line of sight. Multiplication by an absorption cross-section gives an optical depth. A small column can result from a small local density, a small path length, or a small fraction of atoms in the absorbing state, so density inference requires these quantities to be constrained.

Electron number density is the number of free electrons per unit volume. In fully ionized stellar matter, $n_e=\rho /({\mu }_e{m}_u)$, with mass density $\rho$ and mean molecular weight per electron ${\mu }_e$.

The energy density is energy per unit volume. A homogeneous particle species with one-particle energy $E(\mathbf{p})$ has

For an isotropic gas, averaging the momentum flux over directions gives