  We study admittance and energy dissipation in an out-of-equlibrium single
electron box. The system consists of a small metallic island coupled to a
massive reservoir via single tunneling junction. The potential of electrons in
the island is controlled by an additional gate electrode. The energy
dissipation is caused by an AC gate voltage. The case of a strong Coulomb
blockade is considered. We focus on the regime when electron coherence can be
neglected but quantum fluctuations of charge are strong due to Coulomb
interaction. We obtain the admittance under the specified conditions. It turns
out that the energy dissipation rate can be expressed via charge relaxation
resistance and renormalized gate capacitance even out of equilibrium. We
suggest the admittance as a tool for a measurement of the bosonic distribution
corresponding collective excitations in the system.
