Thermodynamics of complex systems: principles and applications

Abstract

In his monograph, Pokrovskii gives an introduction to thermodynamics and the methods used to treat them, before extending the same approach and philosophy to a number of chemical, biological, and social structures. First, an accessible exposition of rudimentary thermodynamics is given, for those previously less acquainted with them, before proceeding to categorise equilibrium and nonequilibrium states, in dense introductory chapters. Following attention to the concept of the internal variables of a system, Pokrovskii’s contribution clarifies the relation of the several microstates of a system to its global state and equilibrium, demonstrating the power of statisticalmechanics. Entropy, to be understood, requires some consideration, from different perspectives, and thus the treatment that it receives here is beneficial. Alongside the rigorous definition of the concept, it would help to have further expansion upon the intuitive representations of it. Then, the tone shifts from a purely rigorous to a more creative one, and the multifarious applications of the fundamental principles discussed are illustrated, with extensive referencing of several works on the topics, including the author’s own. One standard instance of the statistical mechanical method of averaging over micro-scale phenomena to study global evolution is the well-known set of equations of fluid dynamics, which are usefully derived. Building upon ideas of entropy, complexity, and information, the exposition then turns to how complexity is produced, through the imposition and production of order, such as in manufacturing, and via biological evolution. Towards the end, an insightful link with population dynamics is shown, for those concerned with mathematical biology, leading into an application of thermodynamic ideas to that most curious of creatures, man. In turning towards anthropological structures, in which individuals are all agents contributing to the global system, Pokrovskii stretches thermodynamic concepts to apply to social and economic interactions in a novel and imaginative way, seeking to explain theories of Marx and Weber with the same mode of thinking, although the full formalism cannot be fully carried over to these. For later undergraduate students and researchers in the physical sciences, who are knowledgeable of and interested in thermodynamics, and in the associated description of a complex system through the interaction of its microscopic constituent elements, the book offers good instruction. In order to gain most from the mathematical treatment, readers benefit from knowledge of tensor calculus. For those interested and for more advanced readers, the footnotes provide a guide to more complex ideas, such as aspects of microphysics. Although well structured, some typographical errors affect the text. In parts of the book, some issues of translation and imperfections in the English can impair the readability. Incorporating a table of symbols and a glossary could also enhance the presentation.