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Recently, there has been a debate as to whether or not the principle of the identity of indiscernibles (the PII) is compatible with quantum physics. It is also sometimes argued that the answer to this question has implications for the debate over the tenability of ontic structural realism (OSR). The central aim of this paper is to establish what relationship there is (if any) between the PII and OSR. It is argued that one common interpretation of OSR is undermined if the PII turns out to be false, since it is committed to a version of the bundle theory of objects, which implies the PII. However, if OSR is understood as the physical analogue of (sophisticated) mathematical structuralism then OSR does not imply the PII. It is further noted that it is (arguably) a virtue of OSR that it is compatible with a version of the PII for possible worlds.

This article considers the Gibbs paradox and its implications for three definitions of entropy in statistical mechanics: (i) the “classical” Boltzmann entropy (SB1); (ii) the modified Boltzmann entropy that is usually proposed in response to the paradox (SB2); and (iii) a generalized version of the latter (SB2G). It is argued that (i) notwithstanding a recent suggestion to the contrary, the paradox does imply that SB1 is not a satisfactory definition of entropy; (ii) SB2 is undermined by “second-order” versions of the paradox; and (iii) SB2G solves the paradox but is not a satisfactory definition of entropy.

In this paper the spin-echo experiment is examined in the light of three different approaches to statistical mechanics: the coarse-graining Gibbsian approach, the interventionist Gibbsian approach, and the Boltzmannian approach. The conclusions of this examination are almost exactly opposite to the conclusions of Ridderbos and Redhead [1]: Firstly, it is argued that the spin-echo experiment does not tell against a coarsegraining approach to statistical mechanics. Secondly, it is argued that the interventionist approach to statistical mechanics is itself somewhat problematic as its statistical mechanical counterpart of thermodynamic entropy has a number of properties that actual thermodynamic entropy seemingly does not. In the final section of this paper a feature of coarse-grained entropies (their relativity) is noted that may enable coarse-graining approaches to reconcile conflicting intuitions about the behaviour of entropy in the spin-echo experiment, which may be considered a further advantage of such approaches.