I discuss the statistical mechanics of gravitating systems and in particular
its cosmological implications, and argue that many conventional
views on this subject in the foundations of statistical mechanics embody
significant confusion; I attempt to provide a clearer and more accurate
account. In particular, I observe that (i) the role of gravity in entropy
calculations must be distinguished from the entropy of gravity, that (ii)
although gravitational collapse is entropy-increasing, this is not usually
because the collapsing matter itself increases in entropy, and that (iii) the
Second Law of Thermodynamics does not owe its validity to the statistical
mechanics of gravitational collapse.
(PDF) (PostScript)
An investigation is made into how the foundations of statistical mechanics are affected once we treat classical mechanics as an approximation to quantum mechanics in certain domains rather than as a theory in its own right; this is necessary if we are to understand statistical-mechanical systems in our own world. Relevant structural and dynamical differences are identified between classical and quantum mechanics (partly through analysis of technical work on quantum chaos by other authors). These imply that quantum mechanics significantly affects a number of foundational questions, including the nature of statistical probability and the direction of time.
NOTE: though this has been cited quite a bit, for various reasons I've never actually got round to publishing it.
(PDF)
(PostScript)