superextensive

Superextensive is an adjective used to describe a quantity that grows faster than linearly with the size of a system. In thermodynamics and statistical mechanics, many properties are extensive, meaning they scale proportionally with the size of the system (typically the number of constituents N or the volume V). A superextensive property scales as N^α with α greater than 1, or otherwise grows faster than any linear function of N in the thermodynamic limit.

Superextensivity typically arises from long-range interactions, strong correlations, or constraints that destroy simple additivity. For example, in a self-gravitating system, the total energy can scale as N^2 for certain geometries. In some theoretical contexts, black hole entropy scales with area rather than volume, illustrating non-additive scaling that is described in some discussions as superextensive relative to a naive volume-based expectation.

Other quantities, such as certain fluctuations or cumulants, may also display superextensive scaling when correlations persist over large distances or when the system is subject to nonstandard interactions. The term is distinguished from subextensive scaling (slower-than-linear) and from more general non-extensive regimes, which may refer to any deviation from simple linearity.

Mathematically, a property P(N) is superextensive if P(N) ~ c N^α with α > 1 as N → ∞, or if P(N)/N diverges in the thermodynamic limit. The notion depends on the model and interaction range, and in some cases signals a breakdown of standard additive thermodynamics, motivating generalized or non-additive frameworks for describing the system.