  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 one of the particles
called as partial or 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.
