We develop a geometric theory of states arising from the Universal Modular Dynamics (UMD) framework, in which the density operator ρ serves as the fundamental object and geometry is induced by the modular generator K = −log ρ. Within this construction, a Riemannian structure on state space is defined via information-geometric relations, leading to a natural notion of curvature and variational dynamics. We introduce a variational action functional S[ρ] built from geometric and informationtheoretic contributions, and show that it induces a gradient flow on the space of states. This flow defines an intrinsic, irreversible dynamics characterized by a monotonic decrease of S, establishing it as a Lyapunov functional and providing a geometric origin for the arrow of time. Numerical analysis demonstrates that the resulting dynamics generically suppresses offdiagonal coherence and drives states toward a universal attractor corresponding to the maximally mixed configuration. This attractor is shown to be stable under perturbations and independent of initial conditions, thereby identifying classicality as a dynamically emergent and geometrically preferred phase. Importantly, the framework does not rely on external environments, measurement postulates, or stochastic noise. Instead, decoherence and equilibration arise intrinsically from the variational geometry of states defined by UMD. The results suggest that classical behavior can be understood as a universal outcome of geometric state dynamics, providing a novel perspective on irreversibility and the emergence of classicality in quantum systems.