Temperature Dependence of Non-uniformity in Energy of Systems with Holonomic Constraints

For classical systems made of three particles connected with rigid links in thermal equilibrium, the average and variance of the kinetic energies of each particle are exactly obtained. The averages and variances are not uniform over the system but depends on the positions of particles. The excess of average kinetic energies near the chain ends, previously observed by numerical simulation, is analytically proved. The non-uniformity of the average kinetic energy results from the generalized principle of equipartition of energy. For a model with bending potential, the non-uniformity also depends on temperature, and the non-uniformity changes from outer-energetic to inner-energetic by decreasing the temperature.