Integral fluctuation theorem for the housekeeping heat

The housekeeping heat Q(hk) is the dissipated heat necessary to maintain the violation of detailed balance in nonequilibrium steady states. By analysing the evolution of its probability distribution, we prove an integral fluctuation theorem (exp[-beta Q(hk)]) = 1 valid for arbitrary-driven transitions between steady states. We discuss Gaussian limiting cases and the difference between the new theorem and both the Hatano-Sasa and the Jarzynski relation.