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The role of extensive variables in nano-science

We discuss the principle of superposition relative to the definition of extensivity in thermodynamics and discuss how it can be extended to systems that do not obey the linear principle of superposition. This leads to the concept of generalized superposition, of which, there are multiple types defined in the paper. Generalized superposition can be used to explore the breakdown of linearity at the nano-scale, which leads to deeper understanding of nano-materials and nano-thermodynamics.