Sewell G. L. Towards a Macrostatistical Mechanics (134K, TeX) ABSTRACT. I discuss the general question of the derivation of the statistical mechanics of macroscopic variables from the quantum structures of many-particle systems, as represented in the thermodynamic limit. I then present a number of strands of such a macrostatistical mechanics, including (a) a derivation of the electrodynamics of superconductors from their order structure and gauge covariance; (b) a hydrodynamics, with transition from deterministic to stochastic flow, of a quantum plasma model; and (c) a non-linear generalisation of Onsager's irreversible thermodynamics.