  To study the full counting statistics of quantum heat transfer in a driven
nonequilibrium spin-boson model, we develop a generalized nonequilibrium
polaron-transformed Redfield equation with an auxiliary counting field. This
enables us to study the impact of qubit-bath coupling ranging from weak to
strong regimes. Without external modulations, we observe maximal values of both
steady state heat flux and noise power at moderate coupling regimes, below
which we find those two transport quantities are enhanced by the finite qubit
energy bias. With external modulations, the geometric-phase-induced heat flux
shows monotonic decrease as increasing the qubit-bath coupling at zero qubit
energy bias (without bias). While under finite qubit energy bias (with bias),
the geometric-phase-induced heat flux exhibits an interesting reversal behavior
in strong coupling regime. Our results unify the seemingly contradictory
results in weak and strong qubit-bath coupling regimes, and provide detailed
dissections for the quantum fluctuation of nonequilibrium heat transfer.
