Werndl, Charlotte and Frigg, Roman
(2020)
Taming Abundance: on the Relation between Boltzmannian and Gibbsian Statistical Mechanics.
Statistical Mechanics and Scientific Explanation: Determinism, Indeterminism and Laws of Nature.
pp. 617-646.
Abstract
Theoreticians working in statistical mechanics seem to be spoilt for choice. The theory offers two different theoretical approaches, one associated with Boltzmann and the other with Gibbs. These approaches are neither theoretically equivalent nor in any obvious way inter-translatable. This raises the question about the relation between them. We argue that Boltzmannian statistical mechanics is a fundamental theory while the Gibbisan approach is an effective theory, meaning that the former provides a true description of the systems within its scope while the latter offers an algorithm to calculate the values of physical quantities defined by the fundamental theory. This algorithm is often easier to handle than the fundamental theory and provides result where the fundamental theory is intractable. Being an effective theory, the Gibbsian approach works only within a certain domain of application. We provide a characterisation of the limits of the approach and show that BSM provides correct results in cases in which the two theories disagree.
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