nonadditive

Nonadditive describes properties, measures, or effects that cannot be expressed as the simple sum of independent components. In a system partitioned into subsystems A and B, a quantity is additive if value(A ∪ B) = value(A) + value(B) when A and B are disjoint; nonadditive means this equality fails due to interactions or correlations between parts.

In thermodynamics and information theory, nonadditivity arises from interactions among parts or from the mathematical structure of the quantity. Boltzmann–Gibbs entropy is additive for independent subsystems, but generalized entropies such as Tsallis entropy are nonadditive, obeying a pseudo-additivity rule S_q(A ∪ B) = S_q(A) + S_q(B) + (1−q) S_q(A) S_q(B) for independent A and B. Nonadditive measures, or capacities, are monotone set functions used in decision theory and fuzzy probability, where the value of a union is not the sum of the values of its parts.

In mathematics, a nonadditive set function is defined on a collection of sets but does not satisfy additivity for all disjoint pairs. In physics and chemistry, nonadditivity often reflects interaction energy that cannot be decomposed into a sum of fragment energies; for example, total energy in molecular systems includes nonadditive contributions from exchange, correlation, or dispersion that depend on the arrangement of components.

In quantum and statistical models, nonadditivity can refer to cooperative effects among components, yielding outcomes not captured by additive linear models. Recognizing nonadditivity is important for modeling correlations, complex materials, and systems where interactions drive behavior beyond a simple sum of parts.