Critical phenomena and breaking drops: Infinite idealizations in physics

Thermodynamics and Statistical Mechanics are related to one another through the so-called "thermodynamic limit'' in which, roughly speaking the number of particles becomes infinite. At critical points (places of physical discontinuity) this limit fails to be regular. As a result, the "reduction'' of Thermodynamics to Statistical Mechanics fails to hold at such critical phases. This fact is key to understanding an argument due to Craig Callender to the effect that the thermodynamic limit leads to mistakes in Statistical Mechanics. I discuss this argument and argue that the conclusion is misguided. In addition, I discuss an analogous example where a genuine physical discontinuity---the breaking of drops---requires the use of infinite idealizations.
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DOI 10.1016/j.shpsb.2004.05.004
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References found in this work BETA
Craig Callender (2001). Taking Thermodynamics Too Seriously. Studies in History and Philosophy of Science Part B 32 (4):539-553.
Lawrence Sklar (1967). Types of Inter-Theoretic Reduction. British Journal for the Philosophy of Science 18 (2):109-124.

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Robert Batterman (2010). On the Explanatory Role of Mathematics in Empirical Science. British Journal for the Philosophy of Science 61 (1):1-25.

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