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

TL;DR

This paper investigates the energy distribution and emergence of a quasi-equilibrium state in a bead-spring polymer model interacting with a solvent, revealing how energy exchange is hindered in stiff springs and providing insights into system equilibration.

Contribution

It introduces a numerical analysis of energy distribution during quasi-equilibrium in a bead-spring model, highlighting the role of stiff springs in delaying equilibrium and proposing an energy difference as an indicator of inactive degrees.

Findings

Solvent particles have higher kinetic energy than beads in the molecule.

Energy exchange is hindered by stiff springs, prolonging the quasi-equilibrium state.

Energy difference can indicate the system's distance from full equilibrium.

Abstract

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.