Classical Particle Indistinguishability, Precisely
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. This paper is forthcoming in The British Journal for the Philosophy of Science. A preprint may be found here.
Homogeneity and Identity in Thermodynamics
I propose a new representation of the identity relation in thermodynamics using the powerful but little-used geometric formulation. I use it to provide a precise definition of a thermodynamic model and an account of the composite-subsystem relation. The new representation of identity is fully general, and is based on a key assumption in this geometric formulation of thermodynamics: the homogeneity of thermodynamic models, expressing the idea that they ‘look the same’ on all scales. The new criterion of identity is able to recover intuitive results: the composite of two ideal gases which are identical in this sense form an ideal gas of a larger size, while two ideal gases which are non-identical yield a mixture.
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. My argument will turn on a particular philosophical perspective concerning the representational capacities of mathematical structures. I will 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. Adopting Gibbs’ representation leads to a better understanding of the notion of `partial pressure' and of some associated thermodynamic results, Dalton's Law concerning the pressure of a mixture, and Gibbs' Theorem concerning the entropy of a mixture.