We revisit the classical adiabatic law from the perspective of Fisher information geometry. While the link between Fisher information and thermodynamic fluctuations is well established, we show here that the adiabatic exponent \(\upgamma\) admits a new interpretation as quantifying the relative stiffness of energy and volume fluctuations. Within this framework, the law \(PV^\upgamma = \mathrm {const.}\) emerges as a geodesic constraint in thermodynamic state space, providing a conceptual bridge between microscopic fluctuation geometry and macroscopic dynamical invariants. This reinterpretation elevates adiabaticity from a phenomenological rule to an information-theoretic principle, with potential applications to fluctuation control in cold-atom platforms, quantum metrology, and finite-time thermodynamics. Our present results highlight how classical thermodynamic laws can be rederived as emergent signatures of Fisher-geometric structure, opening a pathway toward unifying epistemic and ontic perspectives on thermodynamic order.
