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Generalized Statistical Thermodynamics

Thermodynamics of Probability Distributions and Stochastic Processes

  • Themis┬áMatsoukas
Book

Part of the Understanding Complex Systems book series (UCS)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Themis Matsoukas
    Pages 1-21
  3. Themis Matsoukas
    Pages 23-64
  4. Themis Matsoukas
    Pages 65-97
  5. Themis Matsoukas
    Pages 125-161
  6. Themis Matsoukas
    Pages 163-195
  7. Themis Matsoukas
    Pages 197-239
  8. Themis Matsoukas
    Pages 241-287
  9. Themis Matsoukas
    Pages 289-323
  10. Themis Matsoukas
    Pages 325-348
  11. Back Matter
    Pages 349-363

About this book

Introduction

This book gives the definitive mathematical answer to what thermodynamics really is: a variational calculus applied to probability distributions. Extending Gibbs's notion of ensemble, the Author imagines the ensemble of all possible probability distributions and assigns probabilities to them by selection rules that are fairly general. The calculus of the most probable distribution in the ensemble produces the entire network of mathematical relationships we recognize as thermodynamics.

The first part of the book develops the theory for discrete and continuous distributions while the second part applies this thermodynamic calculus to problems in population balance theory and shows how the emergence of a giant component in aggregation, and the shattering transition in fragmentation may be treated as formal phase transitions.

While the book is intended as a research monograph, the material is self-contained and the style sufficiently tutorial to be accessible for self-paced study by an advanced graduate student in such fields as physics, chemistry, and engineering.

Keywords

statistical thermodynamics population balances The Giant Cluster thermodynamics of continuous distributions the cluster ensemble binary aggregation bicomponent populations

Authors and affiliations

  1. 1.Chemical EngineeringPennsylvania State UniversityUniversity ParkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-04149-6
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-030-04148-9
  • Online ISBN 978-3-030-04149-6
  • Series Print ISSN 1860-0832
  • Series Online ISSN 1860-0840
  • Buy this book on publisher's site
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