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This paper presents an in-depth analysis of the anatomy of boththermodynamics and statistical mechanics, together with the relationshipsbetween their constituent parts. Based on this analysis, using therenormalization group and finite-size scaling, we give a definition of a largebut finite system and argue that phase transitions are represented correctly,as incipient singularities in such systems. We describe the role of thethermodynamic limit. And we explore the implications of this picture ofcritical phenomena for the questions of reduction and emergence.

Becoming Large, Becoming Infinite: The Anatomy of Thermal Physics and Phase Transitions in Finite Systems