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

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.