Interactions never lower the ground state kinetic energy of a quantum system below the noninteracting value. However, at nonzero temperature, where the system occupies a thermal distribution of states, interactions can reduce the kinetic energy. This can be demonstrated from a first order weak coupling expansion. Simulations (both variational and restricted path integral Monte Carlo) of the electron gas model and dense hydrogen confirm this and show that in contrast to the ground state case, at nonzero temperature the population of low momentum states can be increased relative to the free Fermi distribution. This effect is not seen in simulations of liquid He-3.
Phys. Rev. Lett. 89 (2002) 280401.