Virial Theorem

⟨KE⟩ = −½⟨PE⟩ for gravitational/Coulomb systems in steady state

The virial theorem states that for a gravitationally bound system in equilibrium, ⟨KE⟩ = −½⟨PE⟩, so total energy E = ⟨KE⟩ + ⟨PE⟩ = ½⟨PE⟩ < 0. This implies that as a star cluster loses energy (through stellar encounters), it heats up — a negative specific heat. Applied to galaxy clusters by Zwicky in 1933, it provided the first evidence for dark matter.