  We report an experimental and theoretical analysis of the energy exchanged
between two conductors kept at different temperature and coupled by the
electric thermal noise. Experimentally we determine, as functions of the
temperature difference, the heat flux, the out-of- equilibrium variance and a
conservation law for the fluctuating entropy, which we justify theoretically.
The system is ruled by the same equations of two Brownian particles kept at
different temperatures and coupled by an elastic force. Our results set strong
constrains on the energy exchanged between coupled nano-systems kept at
different temperature.}

Statistical Mechanics