Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
On the Einstein relation for a mechanical system
Download PDF
Download PDF
  • Published: April 1997

On the Einstein relation for a mechanical system

  • C. Boldrighini1 &
  • M. Soloveitchik2 

Probability Theory and Related Fields volume 107, pages 493–515 (1997)Cite this article

Abstract.

We consider a mechanical model in the plane, consisting of a vertical rod, subject to a constant horizontal force f and to elastic collisions with the particles of a free gas which is “horizontally” in equilibrium at some inverse temperature β. In a previous paper we proved that, in the appropriate space and time scaling, the motion of the rod is described as a drift term plus a diffusion term. In this paper we prove that the drift d(f) and the diffusivity σ 2 (f) are continuous functions of f, and moreover that the Einstein relation holds, i.e.,

lim f → 0  d(f)f = β2 σ 2 (0) .

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Fisica, Università di Camerino, via Madonna delle Carceri 9, I-62032 Camerino, Italy , , , , , , IT

    C. Boldrighini

  2. Institut für angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 294, D-69120 Heidelberg, Germany, , , , , , DE

    M. Soloveitchik

Authors
  1. C. Boldrighini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Soloveitchik
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Received: 26 January 1996 / In revised form: 2 October 1996

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Boldrighini, C., Soloveitchik, M. On the Einstein relation for a mechanical system. Probab Theory Relat Fields 107, 493–515 (1997). https://doi.org/10.1007/s004400050095

Download citation

  • Issue Date: April 1997

  • DOI: https://doi.org/10.1007/s004400050095

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

  • Mathematics Subject Classification (1991): 60K35
  • 60J27 or 82C05 and 82C31
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature