Quantum fluctuation theorem for heat exchange in the strong coupling regime

We study quantum heat exchange in a multi-state impurity coupled to two thermal reservoirs. Allowing for strong system-bath interactions, we show that a steady-state heat exchange fluctuation theorem holds, though the dynamical processes nonlinearly involve the two reservoirs. We accomplish a closed expression for the cumulant generating function, and use it obtain the heat current and its cumulants in a nonlinear thermal junction, the two-bath spin-boson model.