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

Entropy, dynamics, and molecular chaos.

F Henin1, I Prigogine

  • 1Faculté des Sciences, Université Libre de Bruxelles, Belgium.

Proceedings of the National Academy of Sciences of the United States of America
|July 1, 1974
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

Biology and thermodynamics of irreversible phenomena.

Experientia·2010
Same author

Dynamical roots of time symmetry breaking.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2005
Same author

[Relations between nurses, families and the elderly].

Soins. Gerontologie·1997
Same author

[Caring in a different way...].

Soins. Gerontologie·1996
Same author

[A time to leave].

Soins. Gerontologie·1996
Same author

[Dependency, shame and respect].

Soins. Gerontologie·1996

A new generalized entropy expression, valid for any system preparation, is compared to Boltzmann's formulation. This generalized entropy provides meaningful results in models where Boltzmann's expression fails, offering broader applicability in statistical mechanics.

Area of Science:

  • Statistical Mechanics
  • Probability Theory

Background:

  • Boltzmann's entropy formulation relies on specific assumptions like chaos and Markov processes for the single-particle distribution function.
  • A generalized entropy expression has been recently developed by the research group.

Purpose of the Study:

  • To analyze the generalized entropy expression using probabilistic models (Kac and McKean).
  • To compare the generalized entropy with Boltzmann's entropy formulation.
  • To highlight the limitations of Boltzmann's entropy and the advantages of the generalized approach.

Main Methods:

  • Utilizing simple probabilistic models, specifically Kac and McKean models.
  • Comparing the generalized entropy expression with Boltzmann's entropy based on the single-particle distribution function.

Related Experiment Videos

  • Analyzing the behavior of entropy in different system preparation scenarios.

    • Main Results:

    • The generalized entropy expression is valid irrespective of system preparation, unlike Boltzmann's.
    • In McKean's model, the generalized entropy remains meaningful while Boltzmann's becomes meaningless.
    • In Kac's model, correlations equilibrate faster than the single-particle distribution function, with both formulations converging asymptotically.

    Conclusions:

    • The generalized entropy offers a more robust framework for statistical mechanics, especially when Boltzmann's assumptions are not met.
    • The study demonstrates the limitations of Boltzmann's entropy and the superior applicability of the generalized expression in specific probabilistic models.