Considering a ring which consists of 2N coupled harmonic oscillators, an initial ensemble is introduced, which corresponds to such an initial macroscopic state that a half of the system is at temperature T and the other half is at temperature zero. With this ensemble the average kinetic energy of a particle as a function of time t is calculated. By taking the limit N →∞, it can be concluded that the average value of kinetic energy of each particle approaches the equilibrium value kT/4 as t →∞. These results are compared with the solution of the differential equation of heat flow in an infinite rod.
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Ei Teramoto (1962) studied this question.