Two states do not necessarily correspond to a two-state transition: van’t Hoff enthalpy in the case of a small entropy difference between the states

We discuss the van’t Hoff enthalpy relation, that is conventionally used to determine the two-stateness of a system, in the presence of a small entropy difference between the states. Specifically, for a two-state system we show in this case that the calorimetric enthalpy does not equal the van’t Hoff enthalpy. We also study the van’t Hoff enthalpy for an N-state system and find that the van’t Hoff enthalpy and the calorimetric enthalpy of the N-state system can in fact become equal, provided that the entropy differences between the states are finite.