Jeans equation

The Jeans equations are velocity moments of the Collisionless Boltzmann equation. They relate density, mean motion, velocity dispersion, and gravitational acceleration without requiring a closed fluid equation of state.

For an isolated collisionless system, the tensor virial theorem is $\frac{1}{2}{\ddot{I}}_{jk}=2T_{jk}+{\Pi }_{jk}+W_{jk}$, separating ordered kinetic, random kinetic, and gravitational potential-energy tensors.