Onsager's Non-Equilibrium Thermodynamics as Gradient Flow in Information Geometry

Area of Science:

• Thermodynamics
• Information Geometry
• Statistical Mechanics

Background:

• Onsager's non-equilibrium thermodynamics provides a framework for understanding systems far from equilibrium.
• Information geometry offers a novel perspective for analyzing thermodynamic processes.
• Gradient flow is a powerful mathematical tool for describing dynamic systems.

Purpose of the Study:

• To reformulate Onsager's non-equilibrium thermodynamics using the principles of gradient flow in information geometry.
• To develop and analyze two distinct gradient-flow models based on Onsager's reciprocal relations.
• To apply these models to understand the thermodynamic behavior of ideal and van der Waals gases.

Main Methods:

• Utilizing information geometry to interpret phenomenological equations as gradient flows.
• Deriving two gradient-flow models by incorporating Onsager's reciprocal relations.
• Applying the developed models to specific gas systems (ideal and van der Waals).

Main Results:

• Demonstrated that Onsager's phenomenological equations can be represented as gradient-flow equations.
• Developed two novel gradient-flow models for non-equilibrium thermodynamics.
• Successfully applied these models to analyze the behavior of ideal and van der Waals gases.

Conclusions:

• The gradient flow perspective provides a unified framework for Onsager's non-equilibrium thermodynamics.
• The developed models offer new insights into the dynamics of thermodynamic systems.
• This approach has potential for broader applications in statistical mechanics and beyond.