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

TL;DR

This paper derives exact formulas for the average kinetic energy distribution in a 2D freely jointed chain and a related model, confirming numerical observations and explaining the non-uniformity via the generalized equipartition principle.

Contribution

It provides the first exact analytical expressions for kinetic energies in these models, including the effect of temperature and intra-chain potential.

Findings

Average kinetic energy is higher near chain ends.

Non-uniformity depends on temperature and intra-chain potential.

Analytical results confirm previous numerical observations.

Abstract

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.