Time asymmetric phenomena are successfully predicted by statistical mechanics. Yet the foundations of this theory are surprisingly shaky. Its explanation for the ease of mixing milk with coffee is incomplete, and even implies that un-mixing them should be just as easy. In this book the authors develop a new conceptual foundation for statistical mechanics that addresses this difficulty. Explaining the notions of macrostates, probability, measurement, memory, and the arrow of time in statistical mechanics, they reach the startling conclusion that Maxwell's Demon, the famous perpetuum mobile, is consistent with the fundamental physical laws. Mathematical treatments are avoided where possible, and instead the authors use novel diagrams to illustrate the text. This is a fascinating book for graduate students and researchers interested in the foundations and philosophy of physics.

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Von Neumann argued by means of a thought experiment involving measurements of spin observables that the quantum mechanical quantity$S_{VN}=-k\mathrm{Tr}\,(\rho \mathrm{log}\,\rho) $ is conceptually equivalent to thermodynamic entropy. We analyze Von Neumann's thought experiment and show that his argument fails.

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Statistical mechanics is a strange theory. Its aims are debated, its methods are contested, its main claims have never been fully proven, and their very truth is challenged, yet at the same time, it enjoys huge empirical success and gives us the feeling that we understand important phenomena. What is this weird theory, exactly? Statistical mechanics is the name of the ongoing attempt to apply mechanics (classical, as discussed in this paper, or quantum), together with some auxiliary hypotheses, to explain and predict certain phenomena, above all those described by thermodynamics. This paper shows what parts of this objective can be achieved with mechanics by itself.It thus clarifies what roles remain for the auxiliary assumptions that are needed to achieve the rest of the desiderata. Those auxiliary hypotheses are described in another paper in this journal, Foundations of statistical mechanics: The auxiliary hypotheses.