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Infinite harmonic chains of point particles with finite range translationinvariant interaction have considered. It is assumed that the only one particleinfluenced by the white noise. We studied microscopic and macroscopic behaviorof the system's energies (potential, kinetic, total) when time goes toinfinity. We proved that under quite general condition on interaction potentialthe energies grow linearly with time on macroscopic scale, and grow as $\ln(t)$on microscopic scale. Moreover it is turned out that the system exhibit someequipartition properties in this non equilibrium settings.

Energy Growth of Infinite Harmonic Chain under Microscopic Random Influence