Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Coarse graining from coarse-grained descriptions.

Pep Español1, Federico Vázquez

  • 1Departmento de Física Fundamental, Universidad Nacional de Educación, Madrid, Spain.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|October 8, 2005
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Transfer entropy characterization of causal relations in heat transport near equilibrium.

Physical review. E·2026
Same author

Cost-effectiveness of personalized medical treatment in acromegaly: a post hoc analysis of the ACROFAST study.

Journal of the Endocrine Society·2026
Same author

Decision-making under negativity bias: Double hysteresis in the opinion-dependent q-voter model.

Chaos (Woodbury, N.Y.)·2026
Same author

Acromegaly facial changes analysis using last generation artificial intelligence methodology: the AcroFace system.

Pituitary·2025
Same author

Quality of life and psychological status in people with acromegaly in relation to facial changes.

Endocrine connections·2025
Same author

Unraveling internal friction in a coarse-grained protein model.

The Journal of chemical physics·2025
Same journal

Correction to: 'Stokes settling and particle-laden plumes: implications for deep-sea mining and volcanic eruption plumes' (2020), by Mingotti et al.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

A stable hothouse triggered by a tipping mechanism.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Beyond distance: quantifying point cloud dynamics with persistent homology and dynamic optimal transport.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Global stability of the Atlantic overturning circulation: edge state, long transients and boundary crisis under CO2 forcing.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Morse index classification and landscape of Kuramoto system for Hebbian-based binary pattern recognition.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
Same journal

Interpretable and equation-free response theory for complex systems.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2026
See all related articles

We generalized Zwanzig's projection operator method for non-deterministic dynamics. This allows coarse-graining descriptions where fluctuations matter, resulting in new Fokker-Planck equations for slower dynamics.

Area of Science:

  • Statistical Mechanics
  • Physical Chemistry
  • Non-equilibrium Thermodynamics

Background:

  • Zwanzig's projection operator method is a standard technique for deriving reduced descriptions in statistical mechanics.
  • Existing methods often assume deterministic dynamics, limiting their applicability to systems with significant fluctuations.
  • Coarse-graining is essential for simplifying complex systems but requires careful handling of fluctuations.

Purpose of the Study:

  • To generalize Zwanzig's projection operator method to non-deterministic dynamics.
  • To develop a framework for coarse-graining systems where fluctuations are important.
  • To derive reduced descriptions that retain the essential physics of fluctuations.

Main Methods:

  • Generalization of Zwanzig's projection operator method.

Related Experiment Videos

  • Application to systems described by Fokker-Planck equations.
  • Derivation of a two-level description for colloidal particle diffusion.

    • Main Results:

    • A novel method for coarse-graining non-deterministic dynamics.
    • The generalized method successfully describes systems with important fluctuations.
    • The derived slower dynamics are also described by a Fokker-Planck equation.
    • Successful illustration using colloidal particle diffusion.

    Conclusions:

    • The generalized method provides a powerful tool for analyzing complex systems with fluctuations.
    • This approach allows for a systematic derivation of reduced descriptions from a Fokker-Planck equation to another.
    • The method is applicable to various physical systems where coarse-graining and fluctuations are relevant.