  We use trajectory averaging to show that the energy dissipated in the
nonequilibrium energy-state transitions of a driven two-state system satisfies
a fluctuation-dissipation relation. This connection between the average energy
dissipation induced by external driving and its fluctuations about equilibrium
is preserved by an adiabatic approximation scheme. We use this scheme to obtain
the heat statistics of a single-electron box with superconducting leads in the
slow-driving regime, where the dissipated heat becomes normally distributed
with a relatively high probability to be extracted from the environment rather
than dissipated. We also discuss heat fluctuation relations for driven
two-state transitions.
