James Luscombe - Statistical Mechanics: From Thermodynamics to the Renormalization Group

First edition published 2021

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Library of Congress Cataloging-in-Publication Data

Names: Luscombe, James H., 1954- author.

Title: Statistical mechanics : from thermodynamics to the renormalization group/James Luscombe.

Description: First edition. | Boca Raton : CRC Press, 2021. | Includes bibliographical references and index.

Identifiers: LCCN 2020048146 | ISBN 9781138542976 (paperback) | ISBN 9780367689278 (hardback) | ISBN 9781003139669 (ebook)

Subjects: LCSH: Statistical mechanics.

Classification: LCC QC174.8 .L87 2021 | DDC 530.13dc23

LC record available at https://lccn.loc.gov/2020048146

ISBN: 978-0-367-68927-8 (hbk)

ISBN: 978-1-138-54297-6 (pbk)

ISBN: 978-1-003-13966-9 (ebk)

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To my mother, who likes orderliness, and to my father who didnt. They taught me without trying that the equilibrium state is one of lowest energy and maximum disorder. To my father, who taught me to love the wildness of nature, and to my mother, who taught me to seek order, which I imported into the world of ideas. To my wife, Lisa, who encouraged me, and who lends an order of her own to the written language.To my children, Jennifer and Jimmy, who represent the future and have brought me so much joy.

S TATISTICAL mechanics, a branch of theoretical physics with applications in physics, chemistry, astronomy, materials science, and even biology, relates the observable properties of macroscopic systems to the dynamics of their microscopic constituents. A definition of macroscopicis elusive. Objects indiscernible to human sensesnot ordinarily considered macroscopiccan contain enormous numbers of atoms, Not only are microscopic descriptions impossible, theyre pointless. Even if the wavefunction of NA particles could be found, what would you do with it? Wouldnt you seek to reduce the complexity of the data through some type of averaging procedure? Statistical mechanics provides the means by which averages are calculated for systems in thermal equilibrium.

Historically, statistical mechanics arose from attempts to explain, on mechanistic grounds, the results of thermodynamicsa phenomenological theory of macroscopic systems in thermal equilibrium. A system is said to be in equilibrium when none of its properties appear to be changing in time. The stateof equilibrium is specified by the values of state variablesquantities that can be measured on macroscopic systems. In statistical mechanics, however, the concept of equilibrium is altogether different, where measurable quantities fluctuatein time about mean values. Fluctuations are produced by random motions of the microscopic constituents of matter and are the reason statistical mechanics invokes probability as a fundamental tool.