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We discuss a simple but experimentally realistic model system, asingle-electron box (SEB), where common fluctuation relations can be tested fordriven electronic transitions. We show analytically that when the electronsystem on the SEB island is overheated by the control parameter (gate voltage)drive, the common fluctuation relation (Jarzynski equality) is onlyapproximately valid due to dissipated heat even when the system starts atthermal equilibrium and returns to it after the drive has been stopped.However, an integral fluctuation relation based on total entropy productionworks also in this situation. We perform extensive Monte Carlo simulations ofsingle-electron transitions in the SEB setup and find good agreement with thetheoretical predictions.

Dissipated work and fluctuation relations for non-equilibrium single-electron transitions