Partition of Energy in Chain-Type Systems and Slow Relaxation to Equilibrium: Boltzmann-Jeans Law

Abstract

Partition of energy in chain-type systems where masses are connected by springs or rigid links is investigated. When the chain is composed of masses connected with rigid links, we found that the values of average kinetic energy of the masses are not the same but those which are near to the ends of the chain have larger values than those in the middle of the chain. We clarified that this inhomogeneity results from the generalized equipartition of energy. When the chain is composed of masses connected with springs, average kinetic energies of the masses are the same in the thermal equilibrium. However, inhomogeneity of kinetic energy is observed as transient, then relaxes to homogeneous thermal equilibrium. The relaxation time τ to the equilibrium takes long when the spring constant k is large. We found that τ∝ exp (c√k), which is consistent with Boltzmann-Jeans law. The Boltzmann-Jeans law also holds when the chain is in solvent.