In statistical mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by a conservative force (where the work done is independent of path) with that of the total potential energy of the system. Mathematically, the theorem states ⟨ T ⟩ = − − 1 2 ∑ ∑ k = 1 N ⟨ F k ⋅ ⋅ r k ⟩ where T is the total kinetic energy of the N particles, F k represents the force on the k th particle, which is located at position r k, and angle brackets represent the average over time of the enclosed quantity. The word virial for the right-hand side of the equation derives from vis, the Latin word for "force" or "energy", and was given its technical definition by Rudolf Clausius in 1870.