An Overview on Irreversible Port-Hamiltonian Systems.

Area of Science:

• Thermodynamics
• Mathematical Physics
• Systems Theory

Background:

• Classical port-Hamiltonian systems model energy-preserving systems.
• Irreversible thermodynamic processes require extensions to existing formalisms.
• Coupling mechanical and thermal phenomena presents modeling challenges.

Purpose of the Study:

• To provide a unified formulation for irreversible port-Hamiltonian systems.
• To extend port-Hamiltonian systems to handle irreversible thermodynamic processes.
• To develop a framework for modeling coupled thermo-mechanical systems.

Main Methods:

• Developed an irreversible port-Hamiltonian system formulation.
• Incorporated an energy-preserving and entropy-increasing operator for thermal coupling.
• Utilized co-state variables to define a nonlinear operator dependent on the total energy gradient.
• Demonstrated the formalism on finite and infinite dimensional systems.

Main Results:

• The proposed formulation explicitly couples irreversible mechanical and thermal phenomena.
• The formalism guarantees energy conservation through a skew-symmetric operator.
• The second law of thermodynamics is encoded as a structural property of the system.
• Reversible and conservative systems are shown as a special case.

Conclusions:

• The irreversible port-Hamiltonian system formulation offers a unified approach for diverse thermodynamic systems.
• This framework effectively models coupled thermo-mechanical phenomena and incorporates irreversibility.
• The approach provides a robust mathematical structure for analyzing energy and entropy dynamics.