Exact expression for average kinetic energy of 2-dimensional freely jointed chain and a related model

For a 2-dimensional freely jointed chain with 3 particles and a related model, the average and variance of the kinetic energies of each particle in thermal equilibrium are exactly obtained. The same is done for a related model. The excess of average kinetic energies near the chain ends, previously observed by numerical simulation, is analytically confirmed. The non-uniformity of the average kinetic energy results from the generalized principle of equipartition of energy. The non-uniformity also depends on temperature for a model that has intra-chain potential, and we can control it from outer-energetic to inner-energetic by decreasing the temperature.