Entropy is conventionally regarded as a scalar measure of disorder, while enthalpy is interpreted as the energetic contribution associated with microscopic interactions. This dichotomy underlies the standard decomposition of the Gibbs free energy, yet it obscures the geometric commonality of the mechanisms that produce both terms. Here, we develop a geometric–statistical reformulation of thermodynamic forces in coarse-grained landscapes in which coarse-grained variables evolve on a configuration manifold whose structure encodes the accessible microstates of the system. In isolated systems, this manifold exhibits a degeneracy of free-energy minima corresponding to a Mexican-hat landscape, reflecting maximal entropic freedom along continuous families of equivalent configurations. Coupling to an external environment lifts this degeneracy and deforms the manifold into a thermodynamic paraboloid, whose curvature quantifies the unified thermodynamic stiffness governing system response. We show that enthalpic and entropic contributions to thermodynamic forces arise as orthogonal projections of this local stiffness (Hessian) tensor , thereby revealing a common microscopic origin. As a direct consequence, the well-known enthalpy–entropy compensation phenomenon emerges whenever the curvature of the configuration manifold remains invariant with temperature. This perspective reframes enthalpy and entropy as complementary geometric expressions of the same coarse-grained configuration-space structure. While not intended as a universal description of all thermodynamic systems, it provides a coherent and testable framework for a broad class of physico-chemical processes that admit meaningful collective coordinates and locally harmonic free-energy basins.
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