Identity and indistinguishability in thermal physics

This thesis proposes mathematically precise analyses of the concepts of identity and indistinguishability and explores their physical consequences in thermodynamics and statistical mechanics. I begin by exploring the philosophical consequences of the geometric formulation of thermodynamics, well-known to many mathematicians. Based on this, I offer novel accounts of what it means to be a thermodynamic system and what it means to be a composite system. I then use these mathematical tools to offer new and precise definitions of ‘mixture’ and ‘identity’ in thermodynamics. These analyses allow me to propose a novel resolution of Gibbs’ paradox. Finally, I offer a new definition of indistinguishability in statistical mechanics with a view to offering a new resolution of Gibbs’ paradox in statistical mechanics (the N! problem). My analysis highlights the importance of observables in the foundations of statistical theories. 3