Theorem: p^2 - N k_B T = 0 at Nose-Hoover equipartition

Theorem (Nose-Hoover-equipartition canonical): for NH-thermostatted ideal gas of N particles at T, equipartition gives <p^2/m> = k_B T per DOF, i.e. p^2 = N k_B T for 1-d collective coordinate summing N oscillators. Canonical momentum at…