Works on the Foundations of Statistical Physics

Works on the Foundations of Statistical Physics

NIKOLAI SERGEEVICH KRYLOV
JOEL S. MIGDAL
A. B. Migdal
Ya. G. Sinai
Yu. L. Zeeman
Copyright Date: 1979
Pages: 310
https://www.jstor.org/stable/j.ctt7ztrpd
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  • Book Info
    Works on the Foundations of Statistical Physics
    Book Description:

    Initially published in Moscow in 1950 following the author's death, this book contains the first chapters of a large monograph Krylov planned entitled The foundations of physical statistics," his doctoral thesis on "The processes of relaxation of statistical systems and the criterion of mechanical instability," and a small paper entitled "On the description of exhaustively complete experiments."

    Originally published in 1980.

    ThePrinceton Legacy Libraryuses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

    eISBN: 978-1-4008-5474-5
    Subjects: Physics

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-viii)
  3. PREFACE
    (pp. ix-x)
    A. S. WIGHTMAN
  4. TRANSLATORS’ FOREWORD
    (pp. xi-xii)
    A. B. MIGDAL and YA. G. SINAI

    The book here presented in English translation was published in Moscow in the year 1950 after the death of its author. N. S. Krylov wrote with a certain reticence in a style full of nuance that makes his book as much a work of art as a piece of scientific exposition. It will stir the imagination of everyone who is interested in the problem of the relationship between predetermined and random phenomena.

    N. S. Krylov’s book was undoubtedly far ahead of its time. It is only now that some of its ideas have become clear while others still remain to...

  5. NIKOLAI SERGEEVITCH KRYLOV
    (pp. xiii-xvi)
    V. A. FOCK

    The works of N. S. Krylov, a late physicist from Leningrad, published in this book discuss the problems of laying the foundations of statistical physics. The present volume contains: the first chapters of the large monograph planned by Krylov “The foundations of physical statistics”; his thesis for the doctoral degree, “The processes of relaxation of statistical systems and the criterion of mechanical instability”; and a small paper “On the description of inexhaustively complete experiments.”

    It was the author’s idea that, in addition to some new material, his monograph was to include the content of his doctoral thesis. So the thesis...

  6. THE VIEWS OF N. S. KRYLOV ON THE FOUNDATIONS OF STATISTICAL PHYSICS
    (pp. xvii-2)
    A. B. Migdal and V. A. Fock

    The problem of laying the foundations of physical statistics consists, as is known, in establishing the relationship between statistical laws and micromechanics. This means that it is necessary to derive from micro-mecḥanics the entire range of experimental facts of statistical physics and to provide a criterion of the applicability of statistics to a given mechanical system.

    Experimental results show that following a certain period of time—the relaxation time—a closed macroscopic system approaches a state of statistical equilibrium. Statistical equilibrium manifests itself experimentally in the fact that, for any subsystem, the distribution of states registered at different moments is...

  7. I. THE FOUNDATIONS OF STATISTICAL PHYSICS
    (pp. 3-182)

    The object of this work is to investigate problems related to the general principles of the relaxation of statistical systems. These problems have arisen simultaneously with the problem of what is known as “laying the foundations of statistics,” that is, establishing the connection between physical statistics and mechanics. The difficulties the problem involved were, evidently, of two major types of a totally different nature. In the first place, there were difficulties presented by the need to introduce probabilistic concepts, constituting an essential feature of statistical physics (for example, its basic statement: the H-theorem), into mechanics. In the second place, difficulties...

  8. II. ON THE DESCRIPTION OF INEXHAUSTIVELY COMPLETE EXPERIMENTS
    (pp. 183-192)

    An exhaustively complete experiment is, as is known, an experiment which determines the values of all the simultaneously measurable quantities, that is, in quantum mechanics, of all the quantities corresponding to the mutually commuting operators. An exhaustively complete experiment obviously makes it possible to determine the ψ-function of the system—a vector in the Hilbert space. In the case of an inexhaustively complete experiment, on the other hand, when not all of the simultaneously measurable quantities are measured, only a certain subspace is delimited in the Hilbert space.

    §1. It is commonly believed that inexhaustively complete experiments are described in...

  9. III. THE PROCESSES OF RELAXATION OF STATISTICAL SYSTEMS AND THE CRITERION OF MECHANICAL INSTABILITY (Dissertation for the degree of Doctor of Science)
    (pp. 193-236)

    As is known, all problems involved in what is known as “the laying of the foundations of statistics,” that is, the establishment of the relation between statistics and mechanics, could until recently be reduced to two major difficulties which are totally different in nature: firstly, the difficulty of introducing into classical mechanics probabilistic concepts forming an essential feature of statistical physics, such as, for instance, its basic statement—the H-theorem; secondly, the difficulty of having to define the type of mechanical systems to which the results of statistics can apply. Questions of the first group arise in connection with the...

  10. BIBLIOGRAPHY
    (pp. 237-238)
  11. DEVELOPMENT OF KRYLOV’S IDEAS
    (pp. 239-281)
    Ya. G. Sinai

    In the first chapter of his book Krylov discusses the different approaches to the problem of laying the foundations of statistical physics. The radical conclusion the author comes to is that statistical physics cannot be constructed on the basis of classical or quantum mechanics. While refraining for the moment from examining the substance of that point of view, we shall point out that similar ideas have been put forward by other scientists, too. We can, as an example, refer to the paper by L. Rosenfeld in the book “Ergodic theories” (The International School of Physics “Enrico Fermi,” 1960).

    A considerable...

  12. INDEX
    (pp. 282-283)
  13. Back Matter
    (pp. 284-284)