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Non-Local Vectorial Internal Variables and Generalized Guyer-Krumhansl Evolution Equations for the Heat Flux.

Liliana Restuccia1, David Jou2,3

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This study explores non-local internal variables and their evolution equations in thermodynamic systems. It offers a generalized Guyer-Krumhansl equation for heat transport in nanosystems.

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Area of Science:

  • Thermodynamics
  • Non-local effects in physical systems

Background:

  • Thermodynamic systems often use local internal variables with non-local evolution equations.
  • Non-local differential or integral terms are common in these evolution equations.

Purpose of the Study:

  • Investigate the impact of non-local effects on thermodynamic systems with internal variables.
  • Explore the utility of non-local internal variables and their evolution equations.

Main Methods:

  • Consideration of three key length scales: observation scale (R), mean free path (l), and global system size (L).
  • Analysis of three-dimensional rigid heat conductors under phonon hydrodynamics with thermal vortices.

Main Results:

  • A generalized Guyer-Krumhansl equation is derived.
  • The study examines the interplay between different length scales in non-local descriptions.

Conclusions:

  • Non-local internal variables and evolution equations may offer advantages in specific thermodynamic descriptions.
  • The generalized equation is relevant for heat transport in nanosystems and systems with inhomogeneities.