  We study both experimentally and theoretically the statistical properties of
the energy exchanged between two electrical conductors, kept at different
temperature by two different heat reservoirs, and coupled by the electric
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, the thermodynamic work
done by one part of the system on the other, and 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 theoretically analysis. Our results give
more insight into the energy transfer in the famous Feymann ratchet widely
studied theoretically but never in an experiment.
