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Quantum local-equilibrium approach to dissipative hydrodynamics.

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This study derives macroscopic hydrodynamic equations for many-body quantum systems using a local-equilibrium approach. It demonstrates non-negative entropy production, aligning with thermodynamic laws for fluids and condensed matter.

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Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Hydrodynamics

Background:

  • Macroscopic hydrodynamic equations are crucial for describing fluid behavior.
  • The local-equilibrium approach offers a framework for bridging microscopic and macroscopic descriptions.
  • Quantum mechanics provides the fundamental basis for understanding many-body systems.

Purpose of the Study:

  • To derive macroscopic hydrodynamic equations for many-body systems within the Schrödinger picture.
  • To identify reversible and dissipative parts of current densities and their time evolution.
  • To establish a connection between quantum mechanics and thermodynamic principles.

Main Methods:

  • Utilizing the local-equilibrium approach and the Schrödinger picture.
  • Defining statistical operators based on microscopic densities and macrofields.
  • Applying functional identities and projection-operator methods.
  • Employing the Peierls-Bogoliubov inequality and quantum integral fluctuation theorem.

Main Results:

  • General equations for the time evolution of conjugate macrofields were obtained.
  • The entropy production was proven to be nonnegative.
  • Transport coefficients were expressed via Green-Kubo formulas.
  • Entropy production rate was linked to quantum Einstein-Helfand formulas.

Conclusions:

  • The derived hydrodynamic equations are consistent with the second law of thermodynamics.
  • The framework is applicable to multicomponent fluids and condensed matter with broken symmetries.
  • This work provides a quantum mechanical foundation for macroscopic transport phenomena.