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

We study both experimentally and theoretically the statistical properties of the energy exchanged between two electrical conductors, kept at different temperatures by two different heat reservoirs, and coupled by the electrical thermal noise. Such a system is ruled by the same equations as two Brownian particles kept at different temperatures and coupled by an elastic force. We measure the heat flowing between the two reservoirs and the thermodynamic work done by one part of the system on the other. We show that these quantities exhibit a long-time fluctuation theorem. Furthermore, we evaluate the fluctuating entropy, which satisfies a conservation law. These experimental results are fully justified by the theoretical analysis. Our results give more insight into the energy transfer in the famous Feynman ratchet, widely studied theoretically but never in an experiment.