Stellar systems: what is the difference between virial, dynamical and thermodynamic equilibrium?
Thermal equilibrium

Thermal equilibrium relies strongly on the idea of equipartition of (kinetic) energy. In a stellar system, this means that the total kinetic energy is divided evenly amongst all the stars. This doesn't imply that the velocities are all the same; they can't, because not all the masses are the same.

Dynamical equilibrium

Dynamical equilibrium means that over dynamical timescales, the system is stable - basically, it will not succumb to core collapse due to a gravothermal instability. Note that it may not be possible for a system to reach thermal equilibrium, even if it is in dynamical equilibrium. In a system with two main types of stars, it must satisfy the Spitzer stability condition (see Fregeau et al. (2001) and these results):
$$\left(\frac{M_2}{M_1}\right)\left(\frac{m_2}{m_1}\right)^{3/2}&lt;0.16$$
where $M_1$ and $M_2$ are the total masses of types 1 and 2.

Virial equilibrium

Virial equilibrium comes about when the system satisfies the virial theorem (see Meylan (2000)), i.e.
$$2\langle T\rangle+\langle V\rangle=0$$
where $T$ and $V$ are kinetic and potential energies.