Multibaker map for shear flow and viscous heating.

Area of Science:

• Physics
• Thermodynamics
• Dynamical Systems

Background:

• Understanding shear flow and viscous heating is crucial in fluid dynamics and thermodynamics.
• Existing models often rely on continuum mechanics, with less focus on underlying microscopic dynamics.
• Entropy balance in nonequilibrium systems presents a significant theoretical challenge.

Purpose of the Study:

• To provide a consistent description of shear flow, viscous heating, and entropy balance within a deterministic dynamical system framework.
• To demonstrate the connection between abstract chaotic dynamics and macroscopic thermodynamic equations.
• To explore the incorporation of thermostating algorithms into this dynamical system.

Main Methods:

• Modeling laminar shear flow using a Hamiltonian multibaker map.
• Driving velocity and temperature fields through the dynamical system.
• Analyzing the macroscopic limit to recover established physical equations.
• Incorporating a thermostating algorithm within the dynamical system.

Main Results:

• A consistent framework for shear flow, viscous heating, and entropy balance was established.
• The Hamiltonian multibaker map successfully models the system's behavior.
• The Navier-Stokes and heat conduction equations, along with entropy balance, were recovered in the macroscopic limit.
• The study confirms that chaotic and mixing dynamics can describe nonequilibrium thermodynamics.

Conclusions:

• Deterministic chaotic dynamics provide a valid framework for understanding nonequilibrium thermodynamics.
• The Hamiltonian multibaker map serves as a powerful tool for modeling fluid dynamics and heat transfer.
• This approach offers a microscopic perspective on macroscopic thermodynamic phenomena.