There are three types of reactions that clinopyroxene is involved in and can be used for thermobarometry.
Univariant reactions or displaced equilibria reactions either create or destroy phases within the magma. Each phase will eventually crystalize as a unique mineral. Based on the temperature and pressure conditions, different proportions of these phases will emerge in the final rock. An example reaction is jadeite and quartz reacting to make analbite. Jadeite is a type of pyroxene, so this reaction is used for clinopyroxene barometry.
This particular reaction involves a large change in volume between the reactants and the products, so the reaction is very sensitive to pressure changes.
Exchange Reactions occur when there are minerals with similar structures, and ions switch places with each other within that structure. This is a common method to calculate the temperature because most exchange reactions have a high enthalpy. One example reaction is an exchange of Fe and Mg within garnet and clinopyroxene. That causes pyrope and hedenbergite (pyroxene) to change into almandine and diopside (pyroxene).
Solvus Equilibria reactions occur when two phases dissolve into each other based on the temperature, so it is usually useful for geothermometry. One such reaction is when clinopyroxene and orthopyroxene dissolve into each other. This changes the distribution of calcium and magnesium throughout the mineral.