What Is Gibbs's Canonical Distribution?

Abstract

Although the canonical distribution is one of the central tools of statistical mechanics, the reason for its effectiveness is poorly understood. This is due in part to the fact that there is no clear consensus on what it means to use the canonical distribution to describe a system in equilibrium with a heat bath. I examine some traditional views as to what sort of thing we should take the canonical distribution to represent. I argue that a less explored alternative, according to which the canonical distribution represents a time ensemble of sorts, has a number of advantages that rival interpretations lack.

Ehrenfest and Ehrenfest-Afanassjewa on Why Boltzmannian and Gibbsian Calculations Agree

“…Ehrenfest and Ehrenfest-Afanassjewa opt for the first solution and set out to show that Boltzmannian equilibrium values and Gibbsian phase averages coincide. Their argument is an important one, and similar points have been made more recently by Davey (2009), Myrvold (2016) and Wallace (quoted in Werndl and Frigg forthcoming). They begin by discussing the Gibbsian treatment of the gas with the observable f .…”

Foundations of Statistical Mechanics

“…Since nothing in what follows depends on the exact form of these distributions, we will not state them here. For formal definitions of these distributions, see, for instance, Tolman (1938Tolman ( /1979 and Lavis (2015), and for philosophical discussions, see Davey (2008Davey ( , 2009 and Myrvold (2016).…”

“…Effective theories can do this because they 74 See Frigg (2008b), Sklar (1993), and Uffink (2007) for reviews. 75 See, for instance, Davey (2009), Goldstein (2019), Goldstein, Lebowitz, Tumulka, and Zanghì (2020), and Wallace (2015). 76 See Frigg (2017b, 2020b).…”