Understanding Thermodynamic Singularities: Phase Transitions, Data, and Phenomena

According to standard (quantum) statistical mechanics, the phenomenon of a phase transition, as described in classical thermodynamics, cannot be derived unless one assumes that the system under study is infinite. This is naturally puzzling since real systems are composed of a finite number of particles; consequently, a well-known reaction to this problem was to urge that the thermodynamic definition of phase transitions (in terms of singularities) should not be taken seriously. This article takes singularities seriously and analyzes their role by using the well-known distinction between data and phenomena, in an attempt to better understand the origin of the puzzle.