We derive a class of equations of state for a multi-phase thermodynamic system associated with a finite set of order parameters that satisfy an integrable system of hydrodynamic type. As particular examples, we discuss one-phase systems such as the v
an der Waals gas and the effective molecular field model. The case of N-phase systems is also discussed in detail in connection with entropies depending on the order parameter according to Tsallis composition rule.
