The entropy paradox and overstepping in metamorphic reactions

•Entropy is defined only in equilibrium states, yet is said to increase towards equilibrium.•The resolution of this paradox is the existence of metastable equilibrium states.•Metastable equilibrium states are important both in petrology and in thermodynamics.•In thermodynamics these states depend not on time but on constraint variables.•Thermodynamic affinity also depends on the existence of such states.

It is commonly asserted that entropy tends towards a maximum at equilibrium in isolated systems. But entropy is only defined in equilibrium states, so in an isolated system the entropy is constant, if it is defined at all. The solution to this paradox is the existence of metastable equilibrium states, so common in mineralogy and petrology. Consideration of such states in a thermodynamic context also involves the concept of constraints and of the affinity, and because the affinity is a measure of the change in Gibbs energy in spontaneous reactions involving metastable phases, the entropy paradox and the overstepping of reactions in metamorphic rocks are closely related subjects.