Heat flux and entropy produced by thermal fluctuations.

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 as two Brownian particles kept at different temperatures and coupled by an elastic force. Our results set strong constraints on the energy exchanged between coupled nanosystems held at different temperatures.