In his review of my Time's Arrow and Archimedes' Point ('A la recherche du temps', 29 June, pp. 42--3) Peter Coveney complains that I dismiss non-equilibrium statistical mechanics and chaos theory too quickly. Following Ilya Prigogine's 'Brussels School', Coveney believes that these theories provide the key to the time-asymmetry of thermodynamics -- see for example his own book The Arrow of Time (W H Allen, 1990), written with Roger Highfield.
Like everyone else who tries to apply statistical mechanics to explain why entropy increases irreversibly, the Brussels School is attempting a piece of mathematical magic: to derive an asymmetric result from symmetric mechanical theories (without putting the asymmetry in at the beginning, primitive and unexplained). This is not my main reason for dismissing this approach, however. Its more basic mistake is to misunderstand what is actually puzzling about the thermodynamic arrow. The odd thing is not that entropy is high in the future, but that it is not high at all times. The Brussels methods do a fine job of telling us how non-equilibrium systems behave, given that there are some. However, they tell us nothing about why such systems exist in the first place. As I explain in my book, that's the real mystery of the subject, and the Brussels methods simply don't touch it. (As writers such as Roger Penrose and Stephen Hawking have emphasised, the best current prospects for an explanation lie in cosmology.)
Coveney recommends that my book be read in conjunction with "more broadly based works" on the subject. If his own book on the arrow of time is one of those he has in mind, then I, too, recommend the combination--though partly in the hope that my book will serve as an antidote to some of the confusions of the Brussels School. (In a nice bibliographical symmetry, I reviewed Coveney's The Arrow of Time when it appeared in 1990. Interested readers will find my review in Nature, 348, p. 356, or on the Web.)
School of Philosophy
University of Sydney