Theory Of Macroscopic Systems
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Variational and Extremum Principles in Macroscopic Systems
Recent years have seen a growing trend to derive models of macroscopic phenomena encountered in the fields of engineering, physics, chemistry, ecology, self-organisation theory and econophysics from various variational or extremum principles. Through the link between the integral extremum of a functional and the local extremum of a function (explicit, for example, in the Pontryagin's maximum principle variational and extremum principles are mutually related. Thus it makes sense to consider them within a common context. The main goal of Variational and Extremum Principles in Macroscopic Systems is to collect various mathematical formulations and examples of physical reasoning that involve both basic theoretical aspects and applications of variational and extremum approaches to systems of the macroscopic world. The first part of the book is focused on the theory, whereas the second focuses on applications. The unifying variational approach is used to derive the balance or conservation equations, phenomenological equations linking fluxes and forces, equations of change for processes with coupled transfer of energy and substance, and optimal conditions for energy management. - A unique multidisciplinary synthesis of variational and extremum principles in theory and application - A comprehensive review of current and past achievements in variational formulations for macroscopic processes - Uses Lagrangian and Hamiltonian formalisms as a basis for the exposition of novel approaches to transfer and conversion of thermal, solar and chemical energy
Statistical Thermodynamics
Presenting a look at the modern evolution of statistical thermodynamics, this book provides a detailed overview of the statistical principles used to obtain the physical and thermodynamic properties of macroscopic systems. Going further than many advanced textbooks, it includes Bose-Einstein, Fermi-Dirac statistics, and lattice dynamics as well as applications in polaron theory, electronic gas in a magnetic field, thermodynamics of dielectrics, and magnetic materials in a magnetic field. The text also examines statistical thermodynamics using functional integration and Feynman path integrals. In addition, it features physical results and worked problems.
Entropy and the Time Evolution of Macroscopic Systems
This book is based on the premise that the entropy concept, a fundamental element of probability theory as logic, governs all of thermal physics, both equilibrium and nonequilibrium. The variational algorithm of J. Willard Gibbs, dating from the 19th Century and extended considerably over the following 100 years, is shown to be the governing feature over the entire range of thermal phenomena, such that only the nature of the macroscopic constraints changes. Beginning with a short history of the development of the entropy concept by Rudolph Clausius and his predecessors, along with the formalization of classical thermodynamics by Gibbs, the first part of the book describes the quest to uncover the meaning of thermodynamic entropy, which leads to its relationship with probability and information as first envisioned by Ludwig Boltzmann. Recognition of entropy first of all as a fundamental element of probability theory in mid-twentieth Century led to deep insights into both statistical mechanics and thermodynamics, the details of which are presented here in several chapters. The later chapters extend these ideas to nonequilibrium statistical mechanics in an unambiguous manner, thereby exhibiting the overall unifying role of the entropy.