Steady shear flow thermodynamics based on a canonical distribution approach

Area of Science:

• Non-equilibrium thermodynamics
• Statistical mechanics
• Fluid dynamics

Background:

• Describing shear flow in non-equilibrium steady states requires advanced thermodynamic frameworks.
• Classical mechanics and Lagrangian formalism are foundational for understanding system dynamics.

Purpose of the Study:

• To develop a nonequilibrium steady-state thermodynamics for shear flow.
• To derive thermodynamic stability conditions and a viscosity response formula.
• To introduce a nonequilibrium entropy and validate the approach with simulations.

Main Methods:

• Construction of a canonical distribution for shear flow using Lagrangian mechanics.
• Derivation of the Evans-Hanley shear flow thermodynamics.
• Consistency check with Kawasaki distribution and nonequilibrium molecular-dynamics simulations.

Main Results:

• The Evans-Hanley thermodynamics relates energy, entropy, and shear rate, with viscosity linked to Helfand's moment.
• Thermodynamic stability conditions for shear flow are established, including positivity of a correlation function.
• A viscosity response formula is derived, and simulations support the non-negative power requirement for steady shear flow.

Conclusions:

• The developed canonical distribution approach provides a consistent thermodynamic framework for shear flow.
• The study introduces a novel nonequilibrium entropy that increases with time, equal to the work input.
• This work offers a robust theoretical and computational basis for understanding non-equilibrium fluid behavior.