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

Emergence of Quasi-equilibrium State and Energy Distribution for the Beads-spring Molecule Interacting with a Solvent