Fluctuations of Heat in Driven Two-State Systems: Application to Single-Electron Box with Superconducting Gap

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.