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Reductions and extensions in mesoscopic dynamics.

Miroslav Grmela1, Václav Klika2, Michal Pavelka3

  • 1École Polytechnique de Montréal, C.P. 6079 succ. Centre-ville, Montréal, H3C 3A7 Québec, Canada.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2015
PubMed
Summary
This summary is machine-generated.

This study explores how to simplify or add detail to mesoscopic theories. It formulates methods for reducing complexity or extending models, ensuring compatibility between different levels of detail.

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Area of Science:

  • Physics
  • Theoretical Physics
  • Statistical Mechanics

Background:

  • Mesoscopic theories describe systems with intermediate numbers of particles.
  • Understanding how to change the level of detail in these theories is crucial for modeling complex phenomena.
  • Existing methods for model reduction and extension lack a unified framework.

Purpose of the Study:

  • To develop a general framework for the reduction and extension of mesoscopic theories.
  • To investigate the mathematical structures underlying these transformations.
  • To ensure compatibility between different levels of description in mesoscopic systems.

Main Methods:

  • Formulation of reduction and extension in an abstract mathematical setting.
  • Utilizing time evolution and entropy increase for model reduction.
  • Introducing extra state variables in vector fields for model extension.
  • Defining compatibility relations between reduced and extended levels.

Main Results:

  • A unified mathematical framework for reduction and extension of mesoscopic levels is established.
  • The process of increasing entropy during time evolution is identified as a key mechanism for reduction.
  • Specific examples illustrate the application of the framework in concrete mesoscopic theories.
  • Compatibility conditions ensure consistency across different levels of theoretical detail.

Conclusions:

  • The developed framework provides a rigorous approach to manipulating the level of detail in mesoscopic theories.
  • This work facilitates the connection between different theoretical descriptions of the same physical system.
  • The findings have implications for developing more comprehensive and adaptable mesoscopic models.