Emergent behaviors of two thermodynamically consistent inertial spin models

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Continuum Mechanics

Background:

• The inertial spin model describes the dynamics of particles with spin.
• Existing models may not fully align with thermodynamic consistency and entropy principles.

Purpose of the Study:

• To propose two novel, thermodynamically consistent inertial spin models.
• To generalize existing models for ensembles of mechanical particles with spin.
• To ensure collective dynamics align with the entropy principle.

Main Methods:

• Utilized Hamiltonian formulation and flocking formalism.
• Coupled inertial spin models with temperature based on Ha and Ruggeri's work.
• Developed frameworks for asymptotic analysis.

Main Results:

• The proposed models are thermodynamically consistent.
• Models adhere to the entropy principle.
• Demonstrated asymptotic vanishing of spins and velocity alignment.
• Numerical simulations validated analytical predictions.

Conclusions:

• The new models offer a robust framework for studying spin dynamics.
• Consistency with thermodynamic principles is achieved.
• The models provide insights into collective behavior and alignment phenomena.