Skip to main content

Main menu

  • Home
  • Articles
    • Current
    • Special Feature Articles - Most Recent
    • Special Features
    • Colloquia
    • Collected Articles
    • PNAS Classics
    • List of Issues
  • Front Matter
    • Front Matter Portal
    • Journal Club
  • News
    • For the Press
    • This Week In PNAS
    • PNAS in the News
  • Podcasts
  • Authors
    • Information for Authors
    • Editorial and Journal Policies
    • Submission Procedures
    • Fees and Licenses
  • Submit
  • Submit
  • About
    • Editorial Board
    • PNAS Staff
    • FAQ
    • Accessibility Statement
    • Rights and Permissions
    • Site Map
  • Contact
  • Journal Club
  • Subscribe
    • Subscription Rates
    • Subscriptions FAQ
    • Open Access
    • Recommend PNAS to Your Librarian

User menu

  • Log in
  • My Cart

Search

  • Advanced search
Home
Home
  • Log in
  • My Cart

Advanced Search

  • Home
  • Articles
    • Current
    • Special Feature Articles - Most Recent
    • Special Features
    • Colloquia
    • Collected Articles
    • PNAS Classics
    • List of Issues
  • Front Matter
    • Front Matter Portal
    • Journal Club
  • News
    • For the Press
    • This Week In PNAS
    • PNAS in the News
  • Podcasts
  • Authors
    • Information for Authors
    • Editorial and Journal Policies
    • Submission Procedures
    • Fees and Licenses
  • Submit
Research Article

Fluctuation spectra and force generation in nonequilibrium systems

Alpha A. Lee, Dominic Vella, and John S. Wettlaufer
  1. aSchool of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138;
  2. bMathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom;
  3. cDepartment of Geology and Geophysics, Yale University, New Haven, CT 06520;
  4. dDepartment of Mathematics, Yale University, New Haven, CT 06520;
  5. eDepartment of Physics, Yale University, New Haven, CT 06520;
  6. fNordic Institute for Theoretical Physics, Royal Institute of Technology and Stockholm University, SE-10691 Stockholm, Sweden

See allHide authors and affiliations

PNAS August 29, 2017 114 (35) 9255-9260; first published August 15, 2017; https://doi.org/10.1073/pnas.1701739114
Alpha A. Lee
aSchool of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138;
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • For correspondence: john.wettlaufer@yale.edu alphalee@g.harvard.edu dominic.vella@maths.ox.ac.uk
Dominic Vella
bMathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom;
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • For correspondence: john.wettlaufer@yale.edu alphalee@g.harvard.edu dominic.vella@maths.ox.ac.uk
John S. Wettlaufer
bMathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom;
cDepartment of Geology and Geophysics, Yale University, New Haven, CT 06520;
dDepartment of Mathematics, Yale University, New Haven, CT 06520;
eDepartment of Physics, Yale University, New Haven, CT 06520;
fNordic Institute for Theoretical Physics, Royal Institute of Technology and Stockholm University, SE-10691 Stockholm, Sweden
  • Find this author on Google Scholar
  • Find this author on PubMed
  • Search for this author on this site
  • For correspondence: john.wettlaufer@yale.edu alphalee@g.harvard.edu dominic.vella@maths.ox.ac.uk
  1. Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved July 10, 2017 (received for review January 31, 2017)

  • Article
  • Figures & SI
  • Info & Metrics
  • PDF
Loading

Significance

Understanding force generation in nonequilibrium systems is a significant challenge in statistical and biological physics. We show that force generation in nonequilibrium systems is encoded in their energy fluctuation spectra. In particular, a nonequipartition of energy, which is only possible in active systems, can lead to a nonmonotonic fluctuation spectrum. For a narrow, unimodal spectrum, we find that the force exerted by a nonequilibrium system on two embedded walls depends on the width and the position of the peak in the fluctuation spectrum, and oscillates between repulsion and attraction as a function of wall separation. Our results agree with recent molecular dynamics simulations of active Brownian particles, and shed light on the old riddle of the Maritime Casimir effect.

Abstract

Many biological systems are appropriately viewed as passive inclusions immersed in an active bath: from proteins on active membranes to microscopic swimmers confined by boundaries. The nonequilibrium forces exerted by the active bath on the inclusions or boundaries often regulate function, and such forces may also be exploited in artificial active materials. Nonetheless, the general phenomenology of these active forces remains elusive. We show that the fluctuation spectrum of the active medium, the partitioning of energy as a function of wavenumber, controls the phenomenology of force generation. We find that, for a narrow, unimodal spectrum, the force exerted by a nonequilibrium system on two embedded walls depends on the width and the position of the peak in the fluctuation spectrum, and oscillates between repulsion and attraction as a function of wall separation. We examine two apparently disparate examples: the Maritime Casimir effect and recent simulations of active Brownian particles. A key implication of our work is that important nonequilibrium interactions are encoded within the fluctuation spectrum. In this sense, the noise becomes the signal.

  • Casimir effect
  • nonequilibrium physics
  • fluctuations
  • active matter

Footnotes

  • ↵1To whom correspondence may be addressed. Email: john.wettlaufer{at}yale.edu, alphalee{at}g.harvard.edu, or dominic.vella{at}maths.ox.ac.uk.
  • Author contributions: A.A.L., D.V., and J.S.W. designed research, performed research, analyzed data, and wrote the paper.

  • The authors declare no conflict of interest.

  • This article is a PNAS Direct Submission.

View Full Text
PreviousNext
Back to top
Article Alerts
Email Article

Thank you for your interest in spreading the word on PNAS.

NOTE: We only request your email address so that the person you are recommending the page to knows that you wanted them to see it, and that it is not junk mail. We do not capture any email address.

Enter multiple addresses on separate lines or separate them with commas.
Fluctuation spectra and force generation in nonequilibrium systems
(Your Name) has sent you a message from PNAS
(Your Name) thought you would like to see the PNAS web site.
CAPTCHA
This question is for testing whether or not you are a human visitor and to prevent automated spam submissions.
Citation Tools
Nonequilibrium fluctuation spectra and forces
Alpha A. Lee, Dominic Vella, John S. Wettlaufer
Proceedings of the National Academy of Sciences Aug 2017, 114 (35) 9255-9260; DOI: 10.1073/pnas.1701739114

Citation Manager Formats

  • BibTeX
  • Bookends
  • EasyBib
  • EndNote (tagged)
  • EndNote 8 (xml)
  • Medlars
  • Mendeley
  • Papers
  • RefWorks Tagged
  • Ref Manager
  • RIS
  • Zotero
Request Permissions
Share
Nonequilibrium fluctuation spectra and forces
Alpha A. Lee, Dominic Vella, John S. Wettlaufer
Proceedings of the National Academy of Sciences Aug 2017, 114 (35) 9255-9260; DOI: 10.1073/pnas.1701739114
del.icio.us logo Digg logo Reddit logo Twitter logo CiteULike logo Facebook logo Google logo Mendeley logo
  • Tweet Widget
  • Facebook Like
  • Mendeley logo Mendeley

Article Classifications

  • Physical Sciences
  • Applied Physical Sciences
Proceedings of the National Academy of Sciences: 114 (35)
Table of Contents

Submit

Sign up for Article Alerts

Jump to section

  • Article
    • Abstract
    • Fluctuation Spectrum and Fluctuation-Induced Force
    • Maritime Casimir Effect
    • General Phenomenology of Narrow Unimodal Spectra
    • Force Generation with Active Brownian Particles
    • Conclusion
    • Acknowledgments
    • Footnotes
    • References
  • Figures & SI
  • Info & Metrics
  • PDF

You May Also be Interested in

Setting sun over a sun-baked dirt landscape
Core Concept: Popular integrated assessment climate policy models have key caveats
Better explicating the strengths and shortcomings of these models will help refine projections and improve transparency in the years ahead.
Image credit: Witsawat.S.
Model of the Amazon forest
News Feature: A sea in the Amazon
Did the Caribbean sweep into the western Amazon millions of years ago, shaping the region’s rich biodiversity?
Image credit: Tacio Cordeiro Bicudo (University of São Paulo, São Paulo, Brazil), Victor Sacek (University of São Paulo, São Paulo, Brazil), and Lucy Reading-Ikkanda (artist).
Syrian archaeological site
Journal Club: In Mesopotamia, early cities may have faltered before climate-driven collapse
Settlements 4,200 years ago may have suffered from overpopulation before drought and lower temperatures ultimately made them unsustainable.
Image credit: Andrea Ricci.
Steamboat Geyser eruption.
Eruption of Steamboat Geyser
Mara Reed and Michael Manga explore why Yellowstone's Steamboat Geyser resumed erupting in 2018.
Listen
Past PodcastsSubscribe
Birds nestling on tree branches
Parent–offspring conflict in songbird fledging
Some songbird parents might improve their own fitness by manipulating their offspring into leaving the nest early, at the cost of fledgling survival, a study finds.
Image credit: Gil Eckrich (photographer).

Similar Articles

Site Logo
Powered by HighWire
  • Submit Manuscript
  • Twitter
  • Facebook
  • RSS Feeds
  • Email Alerts

Articles

  • Current Issue
  • Special Feature Articles – Most Recent
  • List of Issues

PNAS Portals

  • Anthropology
  • Chemistry
  • Classics
  • Front Matter
  • Physics
  • Sustainability Science
  • Teaching Resources

Information

  • Authors
  • Editorial Board
  • Reviewers
  • Subscribers
  • Librarians
  • Press
  • Site Map
  • PNAS Updates
  • FAQs
  • Accessibility Statement
  • Rights & Permissions
  • About
  • Contact

Feedback    Privacy/Legal

Copyright © 2021 National Academy of Sciences. Online ISSN 1091-6490