It is a rather unexpected result on the asymmetric fluctuations of the transient heat fluxes between two coupled micro-systems kept at different temperatures. From macroscopic thermodynamics we know that as soon as a temperature difference between two systems is switched on, heat begins to flow from the hot source to the cold one, till the final steady state heat flux is established.

Here we show that in small systems, where thermal fluctuations cannot be neglected, there is a finite probability for the heat to flow from the cold to the hot reservoir. From a theoretical point of view, the probability to observe such rare events is constrained by the Fluctuation Theorem, and this result stresses the statistical interpretation of the second law of thermodynamics. However, the heat currents flowing into the two reservoirs exhibit different statistical properties: the heat flowing from the hot reservoir exhibit the same statistical properties at any time, while the heat flowing from the cold reservoir reaches the steady state only asymptotically.

This result is relevant in describing the transient behavior of micro and nano systems in contact with different thermal baths.

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