  In order to apply thermodynamics to systems in which entropy is not
extensive, it has become customary to define generalized entropies. While this
approach has been effective, it is not the only possible approach. We suggest
that some systems, including nanosystems, can be investigated by instead
generalizing the concept of extensivity. We begin by reexamining the role of
linearity in the definition of complex physical systems. We show that there is
a generalized form of extensivity that can be defined for a number of
non-linear systems. We further show that a generalization of the principle of
linear superposition is the basis for defining generalized extensivity. We
introduce a definition for the the degree of non-extensivity for systems. We
show that generalized extensivity can be used as a means of understanding
complex physical systems and we propose extending the idea extensivity beyond
thermodynamics to other physical systems, including nanosystems.
