  Interactions never lower the ground state kinetic energy of a quantum system.
However, at nonzero temperature, where the system occupies a thermal
distribution of states, interactions can reduce the kinetic energy below the
noninteracting value. 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.

Statistical Mechanics