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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.