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From Lagrangian Mechanics to Nonequilibrium Thermodynamics: A Variational Perspective
François Gay-Balmaz1, Hiroaki Yoshimura2
1Centre National de la Recherche Scientifique (CNRS), Le Laboratoire de Météorologie Dynamique (LMD), Ecole Normale Supérieure, 75005 Paris, France.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
This study extends Hamilton's principle to model irreversible processes in discrete and continuum systems using variational nonequilibrium thermodynamics. The research systematically incorporates friction, heat, and mass transfer for enhanced thermodynamic system analysis.
Area of Science:
- Thermodynamics
- Classical Mechanics
- Continuum Mechanics
Background:
- Classical mechanics relies on Hamilton's principle for reversible processes.
- Thermodynamic systems often involve irreversible processes like friction, heat, and mass transfer.
- Existing models may not fully capture nonequilibrium thermodynamics in complex systems.
Purpose of the Study:
- To present a variational formulation of nonequilibrium thermodynamics.
- To extend Hamilton's principle to encompass irreversible processes.
- To analyze both finite-dimensional discrete and infinite-dimensional continuum systems.
Main Methods:
- Systematic extension of Hamilton's principle.
- Application to thermodynamic systems of increasing complexity.
- Analysis of discrete systems with friction, heat, and mass transfer.
- Illustration using multicomponent Navier-Stokes-Fourier systems for continuum analysis.
Main Results:
- A unified variational framework for nonequilibrium thermodynamics.
- Successful incorporation of irreversible processes in discrete systems (closed and open).
- Demonstration of the theory's applicability to continuum systems.
Conclusions:
- The variational approach provides a powerful tool for studying nonequilibrium thermodynamics.
- The extended Hamilton's principle offers a systematic method for modeling irreversible phenomena.
- The framework is applicable across different system dimensions and complexities.
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