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Geometric Modeling for Control of Thermodynamic Systems.

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Summary
This summary is machine-generated.

Energy and entropy are storage functions in thermodynamic systems. Factorizing entropy production yields quasi-Hamiltonian formulations for stability analysis and control by interconnection.

Keywords:
Liouville geometrycontroldissipativity theoryhomogeneous Hamiltonian dynamicsinterconnectionmacroscopic thermodynamics

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Area of Science:

  • Thermodynamics
  • Control Theory
  • Mathematical Physics

Background:

  • Energy and entropy are fundamental thermodynamic properties.
  • Understanding their behavior as storage functions is key to system analysis.
  • Irreversible processes introduce complexities in thermodynamic modeling.

Purpose of the Study:

  • To conceptualize energy and entropy as storage functions concerning supply rates.
  • To explore the link between entropy production factorization and quasi-Hamiltonian formulations.
  • To apply these formulations for stability analysis and control of thermodynamic systems.

Main Methods:

  • Regarded energy and entropy as storage functions.
  • Factorized irreversible entropy production.
  • Utilized Liouville geometry and contact geometry.
  • Developed port-thermodynamic systems framework.

Main Results:

  • Demonstrated quasi-Hamiltonian formulations derived from entropy production factorization.
  • Showcased the application of these formulations for stability analysis.
  • Defined port-thermodynamic systems using Liouville geometry.
  • Enabled control by interconnection of thermodynamic systems.

Conclusions:

  • Energy and entropy can be effectively treated as storage functions.
  • Quasi-Hamiltonian formulations offer a powerful tool for thermodynamic system analysis and control.
  • The port-thermodynamic systems approach facilitates interconnection and control strategies.