Elementary Principles in Statistical Mechanics

ISBN: 9789386677143
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In this book, Gibbs carefully showed how the laws of thermodynamics would arise exactly from a generic classical mechanical system, if one allowed for a certain natural uncertainty about the state of that system. The themes of thermodynamic connections to statistical mechanics had been explored in the preceding decades with Clausius, Maxwell, and Boltzmann together writing thousands of pages on this topic. One of Gibbs' aims in writing the book was to distill these results into a cohesive and simple picture (Gibbs wrote in 1892 to his colleague Lord Rayleigh, "Just now I am trying to get ready for publication something on thermodynamics from the priori point of view, or rather on 'statistical mechanics'. I do not know that I shall have anything particularly new in substance, but shall be contented if I can so choose my standpoint (as seems to me possible) as to get a simpler view of the subject."). He had been working on this topic for some time, at least as early as 1884 when he produced a paper (now lost except for its abstract) on the topic of statistical mechanics. Gibbs' book simplified statistical mechanics into a treatise of 207 pages. At the same time, Gibbs fully generalized and expanded statistical mechanics into the form in which it is known today. Gibbs showed how statistical mechanics could be used even to extend thermodynamics beyond classical thermodynamics, to systems of any number of degrees of freedom (including microscopic systems) and non-extensive systems. At the time of the book's writing, the prevailing understanding of nature was purely in classical terms as quantum mechanics had not yet been conceived; even basic facts taken for granted today (such as the existence of atoms) were still contested among scientists. Gibbs was careful in assuming the least about the nature of physical systems under study, and as a result the principles of statistical mechanics laid down by Gibbs have retained their accuracy (with some changes in detail but not in theme), in spite of the major upheavals of modern physics during the early 20th & 21st Century

Topics Covered

  • General Notions. The Principle of Conservation of Extension-in-phase
  • Application of The Principle of Conservation of Extension-in-phase To The Theory of Errors
  • Application of The Principle of Conservation of Extension-in-phase to The Integration
    of The Differential Equations of Motion
  • On The Distribution-inphase Called Canonical, In Which The Index of Probability is
    A Linear Function of The Energy
  • Average Values in A Canonical Ensemble of Systems
  • Extension-in-configuration and Extension-in-velocity,
  • Farther Discussion of Averages in A Canonical Ensemble of Systems
  • On Certain Important Functions of The Energies of A System
  • The Function and The Canonical Distribution
  • On A Distribution in Phase Called Microcanonical in Which All The Systems Have The Same Energy
  • Maximum and Minimum Properties of Various Distributions in Phase
  • On The Motion of Systems and Ensembles of Systems Through Long Periods of Time
  • Effect of Various Processes on An Ensemble of Systems
  • Discussion of Thermodynamic Analogies
  • Systems Composed of Molecules
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