Phase transitions are well-understood phenomena in thermodynamics (TD), but it turns out that they are mathematically impossible in finite SM systems. Hence, phase transitions are truly emergent properties. They appear again at the thermodynamic limit (TL), i.e., in infinite systems. However, most, if not all, systems in which they occur are finite, so whence comes the justification for taking TL? The problem is then traced back to the TD characterization of phase transitions, and it turns out that the characterization is (...) the result of serious idealizations which under suitable circumstances approximate actual conditions. (shrink)

This paper discusses the mistake of understanding the laws and concepts of thermodynamics too literally in the foundations of statistical mechanics. Arguing that this error is still made in subtle ways, the article explores its occurrence in three examples: the Second Law, the concept of equilibrium and the definition of phase transitions.

Statistical mechanics is one of the crucial fundamental theories of physics, and in his new book Lawrence Sklar, one of the pre-eminent philosophers of physics, offers a comprehensive, non-technical introduction to that theory and to attempts to understand its foundational elements. Among the topics treated in detail are: probability and statistical explanation, the basic issues in both equilibrium and non-equilibrium statistical mechanics, the role of cosmology, the reduction of thermodynamics to statistical mechanics, and the alleged foundation of the very notion (...) of time asymmetry in the entropic asymmetry of systems in time. The book emphasises the interaction of scientific and philosophical modes of reasoning, and in this way will interest all philosophers of science as well as those in physics and chemistry concerned with philosophical questions. The book could also be read by an informed general reader interested in the foundations of modern science. (shrink)

Robert Batterman examines a form of scientific reasoning called asymptotic reasoning, arguing that it has important consequences for our understanding of the scientific process as a whole. He maintains that asymptotic reasoning is essential for explaining what physicists call universal behavior. With clarity and rigor, he simplifies complex questions about universal behavior, demonstrating a profound understanding of the underlying structures that ground them. This book introduces a valuable new method that is certain to fill explanatory gaps across disciplines.