DRAFT: What is Gibbs’ Canonical Distribution?∗

Although the canonical distribution is one the central tools of statistical mechanics, the reason for its effectiveness is poorly understood. Part of the reason for this is that it not at all obvious what it means to use the canonical distribution to describe a system in equilibrium with a heat bath. In this paper, I examine some traditional suggestions as to what sort of thing we should take the canonical distribution to be. I suggest that a less explored alternative has some advantages that other suggestions do not, and so deserves further attention. I then go on to show that the way in which the canonical distribution is interpreted impacts the manner in which certain technical problems in physics should be approached. These technical problems concern the modeling of heat baths, and the behavior of systems that come into contact with them.