Partial entropy production in heat transport

We consider a system of two Brownian particles (say A and B), coupled to each other via harmonic potential of stiffness constant k. Particle-A is connected to two heat baths of constant temperatures T-1 and T-2, and particle-B is connected to a single heat bath of a constant temperature T-3. In the steady state, the total entropy production for both particles obeys the fluctuation theorem. We compute the total entropy production due to particle-A in the coupled system (partial and apparent entropy production) in the steady state for a time segment tau. When both particles are weakly interacting with each other, the fluctuation theorem for partial and apparent entropy production is studied. We find a significant deviation from the fluctuation theorem. The analytical results are also verified using numerical simulations. Furthermore, we investigate the effect of hidden fast degrees of freedom on the steady state fluctuation theorem for a system of a single Brownian particle coupled to two heat baths of distinct temperatures and dissipation constants, and coupled to a third heat bath of vanishing temperature and dissipation constant.