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Higher-order generalized hydrodynamics: Foundations within a nonequilibrium statistical ensemble formalism.

Carlos A B Silva1, Clóves G Rodrigues2, J Galvão Ramos3

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This study introduces higher-order generalized hydrodynamics for fluids far from equilibrium. It couples kinetic and hydrodynamic descriptions, enabling analysis of complex fluid dynamics across various Knudsen numbers.

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Area of Science:

  • Statistical mechanics
  • Fluid dynamics
  • Non-equilibrium thermodynamics

Background:

  • Generalized hydrodynamics describes fluid motion with variations in space and time.
  • Existing models often struggle to couple kinetic and hydrodynamic descriptions for systems far from equilibrium.
  • Mesoscopic hydrothermodynamics offers a framework for these complex phenomena.

Purpose of the Study:

  • To construct a higher-order generalized hydrodynamics within a nonequilibrium statistical ensemble formalism.
  • To enable simultaneous treatment of kinetic and hydrodynamic descriptions.
  • To cover fluid dynamics phenomena with short-time and short-space variations and unrestricted Knudsen numbers.

Main Methods:

  • Utilizing a complete thermostatistical approach for systems arbitrarily driven from equilibrium.
  • Deriving a set of coupled nonlinear integrodifferential hydrodynamic equations.
  • Employing a generalized kinetic equation within the nonequilibrium statistical ensemble formalism.

Main Results:

  • Developed a framework for higher-order generalized hydrodynamics (mesoscopic hydrothermodynamics).
  • Successfully coupled kinetic and hydrodynamic descriptions.
  • Derived evolution equations for Grad-like moments of all orders.
  • Identified a hierarchy of Maxwell times relevant for description contraction.

Conclusions:

  • The presented formalism provides a unified approach to fluid dynamics far from equilibrium.
  • The derived equations offer a detailed description of mesoscopic fluid behavior.
  • The hierarchy of Maxwell times aids in simplifying complex models by identifying key variables.