extensivity

Extensivity is a property in thermodynamics and physics describing how certain quantities scale with the size of a system. An extensive property is proportional to the amount of matter or the system’s scale. For a system composed of two subsystems A and B that do not interact in a way that couples their properties, an extensive quantity X satisfies X(A+B) = X(A) + X(B). Consequently, if the system is doubled in size while the intensive conditions (such as temperature and pressure) remain fixed, the extensive properties double as well.

Common examples include mass, volume, total energy, total entropy (in many standard formulations), mole number, and total charge. In contrast, intensive properties such as temperature, pressure, density, and chemical potential do not change with system size.

In statistical mechanics, extensivity emerges when contributions from different parts add up independently. Long-range interactions, correlations, or constraints can lead to deviations from strict additivity, yielding sub-extensive or super-extensive behavior. Some generalized entropy measures, notably Tsallis entropy, are used to model non-extensive systems.

Extensivity provides a simplifying assumption underlying many classical thermodynamic treatments and enables predictable scaling as systems grow. It is a foundational concept in defining the thermodynamic limit and in formulating equations of state for bulk matter.

See also: intensive property, additivity, thermodynamic limit, non-extensive thermodynamics.