I will discuss equilibrium states and the Clausius relation. Consider a system between 2 heat baths with the same inverse temperature. When the temperature is changed, the system will relax to a new equilibrium. The total heat exchanged is finite. When dealing with non-equilibrium stationary states, a constant heat flux is present, and when temperatures are changed, the exchanged heat is proportional with time. However, one is interested in the netto change of heat, which is not proportional with time. It seems that the concept of excess heat captures the netto heat transfer here.