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We focus on the non-equilibrium two-bath spin-boson model, a toy model forexamining quantum thermal transport in many-body open systems. Describing thedynamics within the NIBA equations, applicable, e.g., in the strong system-bathcoupling limit and/or at high temperatures, we derive expressions for thecumulant generating function in both the markovian and non-markovian limits byenergy-resolving the quantum master equation of the subsystem. For a markovianbath, we readily demonstrate the validity of a steady-state heat exchangefluctuation theorem. In the non-markovian limit a "weaker" symmetry relationgenerally holds, a general outcome of microreversibility. We discuss thereduction of this symmetry relation to the universal steady-state fluctuationtheorem. Using the cumulant generating function, an analytic expression for theheat current is obtained. Our results establish the validity of thesteady-state heat exchange fluctuation theorem in quantum systems with strongsystem-bath interactions. From the practical point of view, this study providestools for exploring transport characteristics of the two-bath spin-boson model,a prototype for a nonlinear thermal conductor.

Non-equilibrium spin-boson model: counting statistics and the heat exchange fluctuation theorem