Fluctuations of heat in driven two-state systems: Application to a single-electron box with superconducting gap

By using trajectory averaging to analyze the statistics of energy dissipation in the nonequilibrium energy -state transitions of a driven two-state system, we show that the average energy dissipation induced by external driving is connected to its fluctuations about equilibrium through the simple relation 2kBT (Q) = (delta Q2), which is preserved by an adiabatic approximation scheme. We use this scheme to obtain the heat statistics of a single -electron box with a superconducting lead 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 the validity of heat fluctuation relations beyond driven two-state transitions and the slow-driving regime.