Mathematical Foundations Of Thermodynamics
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| Author | : D.R. Owen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 152 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461395054 |
Research in the past thirty years on the foundations of thermodynamics has led not only to a better understanding of the early developments of the subject but also to formulations of the First and Second Laws that permit both a rigorous analysis of the consequences of these laws and a substantial broadening of the class of systems to which the laws can fruitfully be applied. Moreover, modem formulations of the laws of thermodynamics have now achieved logically parallel forms at a level accessible to under graduate students in science and engineering who have completed the standard calculus sequence and who wish to understand the role which mathematics can play in scientific inquiry. My goal in writing this book is to make some of the modem develop ments in thermodyamics available to readers with the background and orientation just mentioned and to present this material in the form of a text suitable for a one-semester junior-level course. Most of this presentation is taken from notes that I assembled while teaching such a course on two occasions. I found that, aside from a brief review of line integrals and exact differentials in two dimensions and a short discussion of infima and suprema of sets of real numbers, juniors (and even some mature sophomores) had sufficient mathematical background to handle the subject matter. Many of the students whom I taught had very limited experience with formal and rigorous mathematical exposition.
| Author | : R. Giles |
| Publisher | : Elsevier |
| Total Pages | : 252 |
| Release | : 2016-01-22 |
| Genre | : Science |
| ISBN | : 1483184919 |
Mathematical Foundations of Thermodynamics details the core concepts of the mathematical principles employed in thermodynamics. The book discusses the topics in a way that physical meanings are assigned to the theoretical terms. The coverage of the text includes the mechanical systems and adiabatic processes; topological considerations; and equilibrium states and potentials. The book also covers Galilean thermodynamics; symmetry in thermodynamics; and special relativistic thermodynamics. The book will be of great interest to practitioners and researchers of disciplines that deal with thermodynamics, such as physics, engineering, and chemistry.
| Author | : Aleksandr I?Akovlevich Khinchin |
| Publisher | : Courier Corporation |
| Total Pages | : 212 |
| Release | : 1949-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780486601472 |
Phase space, ergodic problems, central limit theorem, dispersion and distribution of sum functions. Chapters include Geometry and Kinematics of the Phase Space; Ergodic Problem; Reduction to the Problem of the Theory of Probability; Application of the Central Limit Theorem; Ideal Monatomic Gas; The Foundation of Thermodynamics; and more.
| Author | : W. Noll |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 330 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642658172 |
German scholars, against odds now not only forgotten but also hard to imagine, were striving to revivify the life of the mind which the mental and physical barbarity preached and practised by the -isms and -acies of 1933-1946 had all but eradicated. Thinking that among the disciples of these elders, restorers rather than progressives, I might find a student or two who would wish to master new mathematics but grasp it and use it with the wholeness of earlier times, in 1952 I wrote to Mr. HAMEL, one of the few then remaining mathematicians from the classical mould, to ask him to name some young men fit to study for the doc torate in The Graduate Institute for Applied Mathematics at Indiana University, flourishing at that time though soon to be destroyed by the jealous ambition of the local, stereotyped pure. Having just retired from the Technische Universitat in Charlottenburg, he passed my inquiry on to Mr. SZABO, in whose institute there NOLL was then an assistant. Although Mr.
| Author | : Michele Campisi |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2021 |
| Genre | : |
| ISBN | : 9783030871642 |
This brief provides a modern pedagogical exposition of the mechanical approach to statistical mechanics initiated by Boltzmann with his early works (1866-1871). Despite the later contribution by Helmholtz, Boltzmann himself (1884-1887), Gibbs, P. Hertz, and Einstein, the mechanical approach remained almost unknown to the modern reader, in favour of the celebrated combinatorial approach, developed by Boltzmann himself during his probabilistic turn (1876-1884). The brief constitutes an ideal continuation of a graduate course of classical mechanics and requires knowledge of basic calculus in many dimension (including differential forms), thermodynamics, probability theory, besides Hamiltonian mechanics. The cornerstone of the whole presentation is the ergodic hypothesis. Special attention is devoted to Massieu potentials (the Legendre transforms of the entropy) which are most natural in statistical mechanics, and also allow for a more direct treatment of the topic of ensemble equivalence.
| Author | : John von Neumann |
| Publisher | : Princeton University Press |
| Total Pages | : 462 |
| Release | : 1955 |
| Genre | : Mathematics |
| ISBN | : 9780691028934 |
A revolutionary book that for the first time provided a rigorous mathematical framework for quantum mechanics. -- Google books
| Author | : Robert Hanlon |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 667 |
| Release | : 2020 |
| Genre | : Science |
| ISBN | : 0198851545 |
At the heart of many fields - physics, chemistry, engineering - lies thermodynamics. While this science plays a critical role in determining the boundary between what is and is not possible in the natural world, it occurs to many as an indecipherable black box, thus making the subject a challenge to learn. Two obstacles contribute to this situation, the first being the disconnect between the fundamental theories and the underlying physics and the second being the confusing concepts and terminologies involved with the theories. While one needn't confront either of these two obstacles to successfully use thermodynamics to solve real problems, overcoming both provides access to a greater intuitive sense of the problems and more confidence, more strength, and more creativity in solving them. This book offers an original perspective on thermodynamic science and history based on the three approaches of a practicing engineer, academician, and historian. The book synthesises and gathers into one accessible volume a strategic range of foundational topics involving the atomic theory, energy, entropy, and the laws of thermodynamics.
| Author | : D.Ya. Petrina |
| Publisher | : CRC Press |
| Total Pages | : 352 |
| Release | : 2002-04-11 |
| Genre | : Science |
| ISBN | : 9780415273541 |
This monograph considers systems of infinite number of particles, in particular the justification of the procedure of thermodynamic limit transition. The authors discuss the equilibrium and non-equilibrium states of infinite classical statistical systems. Those states are defined in terms of stationary and nonstationary solutions to the Bogolyubov equations for the sequences of correlation functions in the thermodynamic limit. This is the first detailed investigation of the thermodynamic limit for non-equilibrium systems and of the states of infinite systems in the cases of both canonical and grand canonical ensembles, for which the thermodynamic equivalence is proved. A comprehensive survey of results is also included; it concerns the properties of correlation functions for infinite systems and the corresponding equations. For this new edition, the authors have made changes to reflect the development of theory in the last ten years. They have also simplified certain sections, presenting them more systematically, and greatly increased the number of references. The book is aimed at theoretical physicists and mathematicians and will also be of use to students and postgraduate students in the field.
| Author | : Axel Kleidon |
| Publisher | : Cambridge University Press |
| Total Pages | : 397 |
| Release | : 2016-03-11 |
| Genre | : Science |
| ISBN | : 1316558592 |
Thermodynamics sets fundamental laws for all physical processes and is central to driving and maintaining planetary dynamics. But how do Earth system processes perform work, where do they derive energy from, and what are the limits? This accessible book describes how the laws of thermodynamics apply to Earth system processes, from solar radiation to motion, geochemical cycling and biotic activity. It presents a novel view of the thermodynamic Earth system explaining how it functions and evolves, how different forms of disequilibrium are being maintained, and how evolutionary trends can be interpreted as thermodynamic trends. It also offers an original perspective on human activity, formulating this in terms of a thermodynamic, Earth system process. This book uses simple conceptual models and basic mathematical treatments to illustrate the application of thermodynamics to Earth system processes, making it ideal for researchers and graduate students across a range of Earth and environmental science disciplines.
| Author | : Georgy Lebon |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 331 |
| Release | : 2008-01-12 |
| Genre | : Science |
| ISBN | : 3540742522 |
Discover the many facets of non-equilibrium thermodynamics. The first part of this book describes the current thermodynamic formalism recognized as the classical theory. The second part focuses on different approaches. Throughout the presentation, the emphasis is on problem-solving applications. To help build your understanding, some problems have been analyzed using several formalisms to underscore their differences and their similarities.
