Why ergodic theory does not explain the success of equilibrium statistical mechanics

We argue that, contrary to some analyses in the philosophy of science literature, ergodic theory falls short in explaining the success of classical equilibrium statistical mechanics. Our claim is based on the observations that dynamical systems for which statistical mechanics works are most likely not ergodic, and that ergodicity is both too strong and too weak a condition for the required explanation: one needs only ergodic-like behaviour for the finite set of observables that matter, but the behaviour must ensure that the approach to equilibrium for these observables is on the appropriate time-scale. 1 Introduction 2 Basic notions and results of ergodic theory 3 The debate over the explanatory relevance of ergodic theory 4 The explanatory irrelevance of ergodic theory 5 Leeds' criticism of the Malament-Zabell strategy 6 Why then does equilibrium statistical mechanics work? 7 Conclusion