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Systems, variational principles and interconnections in non-equilibrium thermodynamics.

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  • 1Centre National de la Recherche Scientifique, Le Laboratoire de Météorologie Dynamique, Ecole Normale Supérieure, Paris, France.

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This study introduces a new way to model non-equilibrium thermodynamics using interconnected systems and a novel Lagrangian variational formulation. This approach offers a unifying framework for various scientific disciplines.

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Area of Science:

  • Thermodynamics
  • Variational Mechanics
  • Complex Systems Modeling

Background:

  • Non-equilibrium thermodynamics lacks a systematic modeling approach.
  • Interconnected systems are a known tool for complex system modeling in networks and mechanics.
  • Bridging natural and social sciences requires new thermodynamic frameworks.

Purpose of the Study:

  • To develop a systematic approach to modeling non-equilibrium thermodynamics.
  • To propose a novel Lagrangian variational formulation for interconnected thermodynamic systems.
  • To explore a unifying framework for diverse scientific areas using thermodynamic principles.

Main Methods:

  • Extending Hamilton's variational principle to non-equilibrium thermodynamics.
  • Modeling thermodynamic systems as interconnected subsystems.
  • Utilizing a Lagrangian variational formulation.

Main Results:

  • A novel Lagrangian variational formulation for interconnected non-equilibrium thermodynamic systems was developed.
  • Demonstrated that non-equilibrium thermodynamic systems can be viewed as interconnected subsystems.
  • Established a connection between modern thermodynamics and early variational mechanics.

Conclusions:

  • The proposed approach offers a promising direction for unifying descriptions across scientific fields.
  • The framework provides a new perspective on modeling complex thermodynamic systems.
  • This work bridges concepts from variational mechanics and non-equilibrium thermodynamics.