Work, Free Energy and Dissipation in Voltage Driven Single-Electron Transitions

We apply the general procedure presented by Jarzynski (C.R. Phys. 8:495, 2007) to the problem of dissipation in a voltage-driven single-electron box. We obtain the expression of dissipated work, and find its relation to the dissipation Q obtained in Averin and Pekola (Europhys. Lett. 96:67004, 2011). We show that the two quantities are identical in common gate protocols where the system makes a transition for sure.