Statistical properties of the heat flux between two nonequilibrium steady-state thermostats

We address the question of transport heat, in out-of-equilibrium systems. The experimental set-up consists two coupled granular gas Non-Equilibrium Steady State (NESS) heat baths, which Brownian-like rotors are imbedded. These electro-mechanically thanks to DC micro-motors, through a resistor $R$, such that energy flows between them. average flux depends linearly difference baths' temperature. Varying $R$ allows extrapolate non-dissipative coupling limit ($R\rightarrow0$). show that, this limit, obeys Fluctuation Theorem, form proposed by Jarzynski and W\'ojcik $2004$ for fluctuations finite size equilibrium baths.