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Area of Science:

  • Thermodynamics
  • Fluid Dynamics
  • Statistical Mechanics

Background:

  • Understanding hydrodynamic transport is crucial for many physical systems.
  • The second law of thermodynamics imposes fundamental constraints on transport processes.
  • Previous work has established constraints on leading-order dissipative terms.

Purpose of the Study:

  • To provide a complete characterization of hydrodynamic transport.
  • To analyze transport consistent with the second law of thermodynamics at arbitrary orders.
  • To investigate the role of adiabatic hydrodynamics in isolating dissipative transport.

Main Methods:

  • Utilizing the concept of adiabatic hydrodynamics.
  • Performing gradient expansion analysis.
  • Characterizing transport properties at arbitrary orders.

Main Results:

  • Demonstrated that the majority of hydrodynamic transport is adiabatic.
  • Identified that only leading-order terms in the gradient expansion of dissipative transport are sign-definite due to the second law.
  • Provided a comprehensive framework for analyzing thermodynamic consistency in transport.

Conclusions:

  • Adiabatic hydrodynamics is a powerful tool for analyzing transport phenomena.
  • The second law of thermodynamics places specific, order-dependent constraints on dissipative transport.
  • This work offers a more complete understanding of thermodynamic limitations on hydrodynamics.