I present a new perspective on the meaning of indistinguishability of classical particles. This leads to a solution to the problem in statistical mechanics of justifying the inclusion of a factor N! in a probability distribution over the phase space of N indistinguishable classical particles.

I describe two candidate representations of a mixture. The first, which I call the ‘standard representation’, is not a good representation of a mixture in spite of its widespread popularity. The second, which I call ‘Gibbs’ representation’, is less widely adopted but is, I argue, a much better representation. I show that, once we have a precise mathematical structure that can be used to represent thermodynamic systems, and once an adequate perspective on representation is adopted, Gibbs’ representation trumps the standard (...) representation. (shrink)