Variational principles in nonequilibrium thermodynamics

Area of Science:

• Thermodynamics
• Statistical Mechanics

Background:

• Onsager's foundational work in nonequilibrium thermodynamics.
• The need for variational principles to describe complex systems.

Purpose of the Study:

• To explore and extend Onsager's variational principles.
• To develop new variational formulations for linear laws.
• To investigate fluctuation descriptions far from equilibrium.

Main Methods:

• Application of Hamiltonian and Lagrangian formulations.
• Utilizing Onsager-Machlup type variational methods.

Main Results:

• Introduction of novel variational formulations for linear laws.
• Demonstration of applicability of Onsager-Machlup methods to steady states.
• Extension of variational principles to systems far from equilibrium.

Conclusions:

• New variational principles offer powerful tools for nonequilibrium thermodynamics.
• These principles are applicable to a broader range of systems, including those far from equilibrium.
• Provides a framework for understanding fluctuations in steady states.