  We study the energy distribution during the emergence of a quasi-equilibrium
(QE) state in the course of relaxation to equipartition in slow-fast
Hamiltonian systems. A bead-spring model where beads (masses) are connected by
springs is considered, and it is used as a model of polymers. The QE lasts for
a long time because the energy exchange between the high-frequency vibrational
and other motions is prevented when springs in the molecule become stiff. We
numerically calculated the time-averaged kinetic energy and found that the
kinetic energy of the solvent particles was always higher than that of the bead
in a molecule. This is explained by adapting the equipartition theorem in QE,
and it agrees well with the numerical results. The energy difference can help
determine how far the system is from achieving equilibrium, and it can be used
as an indicator of the number of frozen or inactive degrees exist in the
molecule.
