Topology of Accessibility in Thermodynamic Geometry: A PQF Reinterpretation of Mrugała's Framework

This editorial note introduces and contextualizes Yochanan Schimmelpfennig’s Topology of Accessibility in Thermodynamic Geometry: A PQF Reinterpretation of Mrugała’s Framework. The work proposes a conceptual and mathematical shift from equilibrium-based thermodynamics to a topology of dynamic accessibility, where systems are defined not by static energy states but by the evolving structure of possible transformations. At the heart of this reinterpretation is the recursive accessibility operator \delta^*, which updates the space of possibilities rather than tracing trajectories in time. The framework reframes irreversibility as a topological asymmetry, and treats chaos and decoherence as intrinsic, structural properties of accessibility fields. By bridging advanced mathematical physics with continental philosophy, this contribution opens a new “grammar of reality” in which potentiality and process take precedence over energy and state, offering a unifying perspective for applications ranging from biophysics to machine learning and the foundations of time. Significance Schimmelpfennig’s reinterpretation of Mrugała’s thermodynamic geometry is significant because it moves beyond the equilibrium-state paradigm, introducing a formalism that treats accessibility as the primary descriptor of a system’s reality. This allows irreversibility, chaos, and complexity to be understood as geometric and topological features rather than purely statistical or temporal effects. By aligning with process philosophy, the framework also opens pathways for cross-disciplinary research, linking abstract mathematics to conceptual tools for understanding change, emergence, and the generative structure of possibility itself. Its mathematical precision combined with philosophical depth makes it a potential cornerstone for new approaches to modeling complex, adaptive, and non-equilibrium systems.