Preservation of thermodynamic structure in model reduction

Area of Science:

• Thermodynamics
• Statistical Mechanics
• Computational Physics

Background:

• Complex systems often require model reduction for tractability.
• Preserving fundamental structures like thermodynamics is crucial during reduction.
• The Kramers problem models barrier crossing phenomena.

Purpose of the Study:

• To develop a model-reduction procedure that preserves thermodynamic structure.
• To apply this procedure to the Kramers problem.
• To analyze the inheritance of emergent properties in reduced models.

Main Methods:

• Utilizing invariant manifolds for model reduction.
• Constructing Poisson and irreversible brackets for nonequilibrium thermodynamics.
• Applying constraint-handling techniques to general equations.

Main Results:

• A model-reduction procedure preserving thermodynamic structure was developed.
• The method was successfully applied to the Kramers problem.
• A logarithmic entropy's ability to generate a linear diffusion equation was shown to be inherited by the reduced master equation.

Conclusions:

• Model reduction preserving thermodynamic structure is feasible.
• The developed method offers insights into Kramers' problem and barrier crossing dynamics.
• Emergent properties in reduced models can be systematically understood.