The partition function of an oscillator disturbed by a set of electron particle paths has been computed by a path integral formalism which permits to evaluate at any temperature the relevant cumulant terms in the series expansion. The low temperature cutoffs in the anharmonic cumulant series are determined fulfilling the constraint of the third law of thermodynamics. The general method here proposed has been applied to the semiclassical Su-Schrieffer-Heeger model whose time dependent source current is linear in the oscillator displacement field. We find that this peculiar current induces large electron-phonon anharmonicities on the phonon subsystem. As a signature of anharmonicity the phonon heat capacity shows a peak whose temperature location strongly varies with the strength of the e-ph coupling. Since the electron hopping potential provides a sizeable background in the low and intermediate temperature range, such a peak is partly smeared in the total heat capacity. Low energy oscillators are more sensitive to anharmonic perturbations. Copyright Springer-Verlag Berlin/Heidelberg 2004
