Wallace, David
(2018)
The Necessity of Gibbsian Statistical Mechanics.
[Preprint]
Abstract
In discussions of the foundations of statistical mechanics, it is widely held that (a) the Gibbsian and Boltzmannian approaches are incompatible but empirically equivalent; (b) the Gibbsian approach may be calculationally preferable but only the Boltzmannian approach is conceptually satisfactory. I argue against both assumptions. Gibbsian statistical mechanics is applicable to a wide variety of problems and systems, such as the calculation of transport coefficients and the statistical mechanics and thermodynamics of mesoscopic systems, in which the Boltzmannian approach is inapplicable. And the supposed conceptual problems with the Gibbsian approach are either misconceived, or apply only to certain versions of the Gibbsian approach, or apply with equal force to both approaches. I conclude that Boltzmannian statistical mechanics is best seen as a special case of, and not an alternatve to, Gibbsian statistical mechanics.
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