Slow relaxation to equipartition in spring-chain systems

Abstract

In this study, one-dimensional systems of masses connected by springs, i.e., spring-chain systems, are investigated numerically. The average kinetic energy of chain-end particles of these systems is larger than that of other particles, which is similar to the behavior observed for systems made of masses connected by rigid links. The energetic motion of the end particles is, however, transient, and the system relaxes to thermal equilibrium after a while, where the average kinetic energy of each particle is the same, that is, equipartition of energy is achieved. This is in contrast to the case of systems made of masses connected by rigid links, where the energetic motion of the end particles is observed in equilibrium. The timescale of relaxation estimated by simulation increases rapidly with increasing spring constant. The timescale is also estimated using the Boltzmann-Jeans theory and is found to be in quite good agreement with that obtained by the simulation.

References in corpus (3)

• Long-Time Correlations in the Stochastic Regime
• Self-Organized Bottleneck in Energy Relaxation
• Roundabout relaxation: collective excitation requires a detour to equilibrium

Cited by in corpus (5)

• Equilibration of energy in slow-fast systems
• Strange Scaling and Temporal Evolution of Finite-Size Fluctuation in Thermal Equilibrium
• Apparent violation of equipartition of energy in constrained dynamical systems
• Multiple pendulum and nonuniform distribution of average kinetic energy
• Emergence of Quasi-equilibrium State and Energy Distribution for the Beads-spring Molecule Interacting with a Solvent