Generalized Extensivity

TL;DR

This paper proposes a new approach to analyzing complex systems by generalizing the concept of extensivity, extending beyond traditional thermodynamics to include nanosystems and non-linear systems.

Contribution

It introduces a generalized form of extensivity based on a generalized superposition principle, applicable to non-linear and nanoscale systems.

Findings

Defined a measure for the degree of non-extensivity.

Demonstrated applicability to nanosystems.

Extended the concept of extensivity beyond thermodynamics.

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.