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Dissipation in Laplacian fields across irregular boundaries.

K Karamanos1, G Nicolis, T Massart

  • 1Centre for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Campus Plaine, Code Postal 231, Boulevard du Triomphe, B-1050 Brussels, Belgium.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 20, 2001
PubMed
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Entropy production in Laplacian fields is analyzed. Fractal surfaces show reduced entropy production with increased complexity, suggesting less dissipation in natural fractal structures.

Area of Science:

  • Thermodynamics
  • Fractal Geometry
  • Mathematical Physics

Background:

  • Entropy production is a fundamental concept in thermodynamics, quantifying irreversibility.
  • Laplacian fields are common in physical phenomena, often interacting with complex boundaries.
  • Fractal geometry describes irregular shapes found extensively in nature.

Purpose of the Study:

  • To investigate entropy production for Laplacian fields across irregular boundaries.
  • To derive an explicit expression for entropy production related to geometric properties.
  • To explore the relationship between fractal geometry and thermodynamic dissipation.

Main Methods:

  • Utilizing the active zone approximation.
  • Deriving an explicit expression for entropy production based on geometric features.

Related Experiment Videos

  • Analyzing the impact of successive prefractal generations on entropy production.

    • Main Results:

    • An explicit expression for entropy production in terms of geometry was derived.
    • Entropy production was found to decrease with successive prefractal generations.
    • The final fractal object is expected to dissipate less energy than its predecessors.

    Conclusions:

    • The study provides a quantitative link between geometry and dissipation in fractal systems.
    • The findings suggest that natural fractal surfaces may be more efficient in energy dissipation than previously assumed.
    • This has implications for understanding the prevalence and function of fractal structures in nature.