Entropy is only approximately aggregatible

In classical thermodynamics, entropy is treated much as other physical quantities. In particular, it is treated as if it were additive (and therefore aggregatible), at least during reversible processes. The more precise information-theoretic definition of entropy due to Shannon is not aggregatible in general,as we show here. Just as aggregatibles arise naturally over Boolean algebras, entropies arise naturally over partition lattices. Partition lattices are more complicated than Boolean algebras, in general, and so entropies behave more complicatedly than aggregatibles. However, under certain circumstances common in physics, entropies become approximately aggregatible.