Geometric Foundation of Microcanonical Thermodynamics
Analysis
This paper offers a novel geometric perspective on microcanonical thermodynamics, deriving entropy and its derivatives from the geometry of phase space. It avoids the traditional ensemble postulate, providing a potentially more fundamental understanding of thermodynamic behavior. The focus on geometric properties like curvature invariants and the deformation of energy manifolds offers a new lens for analyzing phase transitions and thermodynamic equivalence. The practical application to various systems, including complex models, demonstrates the formalism's potential.
Key Takeaways
- •Develops a geometric foundation for microcanonical thermodynamics.
- •Entropy and its derivatives are derived from phase space geometry.
- •Phase transitions are linked to geometric reorganizations.
- •Reveals thermodynamic covariance and geometric microcanonical equivalence.
- •Demonstrates practical application across various physical systems.
“Thermodynamics becomes the study of how these shells deform with energy: the entropy is the logarithm of a geometric area, and its derivatives satisfy a deterministic hierarchy of entropy flow equations driven by microcanonical averages of curvature invariants.”