  Through extended consideration of two wide classes of case studies -- dilute
gases and linear systems -- I explore the ways in which assumptions of
probability and irreversibility occur in contemporary statistical mechanics,
where the latter is understood as primarily concerned with the derivation of
quantitative higher-level equations of motion, and only derivatively with
underpinning the equilibrium concept in thermodynamics. I argue that at least
in this wide class of examples, (i) irreversibility is introduced through a
reasonably well-defined initial-state condition which does not precisely map
onto those in the extant philosophical literature; (ii) probability is
explicitly required both in the foundations and in the predictions of the
theory. I then consider the same examples, as well as the more general context,
in the light of quantum mechanics, and demonstrate that while the analysis of
irreversibility is largely unaffected by quantum considerations, the notion of
statistical-mechanical probability is entirely reduced to quantum-mechanical
probability.
