skip to main content
Idioma:

Ergodic theorem, ergodic theory, and statistical mechanics

Moore, Calvin C.

Proceedings of the National Academy of Sciences - PNAS, 2015-02, Vol.112 (7), p.1907-1911 [Periódico revisado por pares]

United States: National Academy of Sciences

Texto completo disponível

Citações Citado por
  • Título:
    Ergodic theorem, ergodic theory, and statistical mechanics
  • Autor: Moore, Calvin C.
  • Assuntos: Mathematical problems ; PERSPECTIVE ; Physical Sciences ; Statistical mechanics ; Theorems
  • É parte de: Proceedings of the National Academy of Sciences - PNAS, 2015-02, Vol.112 (7), p.1907-1911
  • Notas: http://dx.doi.org/10.1073/pnas.1421798112
    ObjectType-Article-1
    SourceType-Scholarly Journals-1
    ObjectType-Feature-2
    content type line 23
    Edited by Kenneth A. Ribet, University of California, Berkeley, CA, and approved January 9, 2015 (received for review November 13, 2014)
    Author contributions: C.C.M. wrote the paper.
  • Descrição: This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject—namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics.
  • Editor: United States: National Academy of Sciences
  • Idioma: Inglês
Links
Voltar para lista de resultados

  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

Buscando em bases de dados remotas. Favor aguardar.