Geometric Foundation of Microcanonical Thermodynamics

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.