Quantum local-equilibrium approach to dissipative hydrodynamics

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.