Generalized Extensivity

Abstract: 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.