Integral fluctuation theorem for the housekeeping heat

The housekeeping heat Q is the dissipated heat necessary to maintain the violation of detailed balance in nonequilibrium steady states. By analyzing the evolution of its probability distribution, we prove an integral fluctuation theorem exp[-β Q]=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.