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We investigate the occurrence of heat leakages in overdamped Brownianharmonic systems. We exactly compute the underdamped and overdamped stochasticheats exchanged with the bath for a sudden frequency or temperature switch. Weshow that the underdamped heat reduces to the corresponding overdampedexpression in the limit of large friction for the isothermal process. However,we establish that this is not the case for the isochoric transformation. Wemicroscopically derive the additionally generated heat leakage and relate itsorigin to the initial relaxation of the velocity of the system. Our resultshighlight the limitations of the overdamped approximation for the evaluation ofthe stochastic heat in systems with changing bath temperature.

Heat leakage in overdamped harmonic systems