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We study both experimentally and theoretically the statistical properties ofthe energy exchanged between two electrical conductors, kept at differenttemperature by two different heat reservoirs, and coupled by the electricthermal noise. Such a system is ruled by the same equations as two Brownianparticles kept at different temperatures and coupled by an elastic force. Wemeasure the heat flowing between the two reservoirs, the thermodynamic workdone by one part of the system on the other, and we show that these quantitiesexhibit a long time fluctuation theorem. Furthermore, we evaluate thefluctuating entropy, which satisfies a conservation law. These experimentalresults are fully justified by the theoretically analysis. Our results givemore insight into the energy transfer in the famous Feymann ratchet widelystudied theoretically but never in an experiment.

Statistical properties of the energy exchanged between two heat baths coupled by thermal fluctuations