Critical phenomena and breaking drops: Infinite idealizations in physics

Abstract

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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2009-01-28

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Robert W. Batterman
University of Pittsburgh

References found in this work

Two Concepts of Intertheoretic Reduction.Thomas Nickles - 1973 - Journal of Philosophy 70 (April):181-201.
Taking Thermodynamics Too Seriously.Craig Callender - 2001 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 32 (4):539-553.

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Citations of this work

Minimal Model Explanations.Robert W. Batterman & Collin C. Rice - 2014 - Philosophy of Science 81 (3):349-376.
How Scientific Models Can Explain.Alisa Bokulich - 2011 - Synthese 180 (1):33 - 45.
On the Explanatory Role of Mathematics in Empirical Science.Robert W. Batterman - 2010 - British Journal for the Philosophy of Science 61 (1):1-25.

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