Knotted proteins are harder to unfold than unknotted ones. This has been known experimentally for a decade. The standard interpretation treats the knot as a thermodynamic feature — it stabilizes the native state, making the folded configuration more favorable. Zheng, Coronel, and Rapaport (2026, arXiv:2603.12053) measure both kinetic and thermodynamic stability of knotted proteins separately. The result: the knot increases kinetic stability (resistance to unfolding at a given temperature) proportionally to knot depth. It does not affect thermodynamic stability (the equilibrium melting temperature). A companion study (Coronel, Orlandini, and Bhatt, arXiv:2511.07024) confirms the thermodynamic finding and explains why earlier experiments confused the two — deeply knotted proteins take so long to unknot that short experiments never reach equilibrium. They look thermodynamically stabilized because the kinetics are too slow for the measurement.
The topology creates a barrier in conformational space. Not an energetic preference — a geometric obstacle. The knotted chain must thread through itself to unfold, and the more deeply embedded the knot, the longer the path through the barrier. Foldability is largely unaffected because the folding pathways don't require the reverse threading. The knot acts as a one-way ratchet: easy in, hard out. The asymmetry is geometric, not energetic.
In passive disordered solids — glasses, metallic alloys, granular packings — plastic deformation can be predicted from the energy landscape. Quasilocalized soft spots in the potential energy surface correspond to sites where the material will yield under stress. The framework depends on the system being conservative: forces must derive from a potential. Active matter — dense assemblies of self-propelled particles — violates this. Each particle injects energy continuously. The forces are non-conservative. No energy landscape exists.
Caporusso, Manning, and Morse (2026, arXiv:2603.11425) show that the prediction survives anyway. In dense packings of self-propelled rods, they replace the energy landscape with a force landscape — the eigenstructure of the force field itself, without reference to any underlying potential. The quasilocalized excitations computed from force-based, not energy-based, analysis predict plastic events with the same accuracy as energy-based methods in passive systems. The landscape was always doing the geometric work. The energy was just one way of generating the landscape.
Both results share a structural claim: the geometry outlasts its generating principle. In the protein case, the operative structure is the topology of the conformational barrier. Thermodynamics — the energetic framework that was presumed to explain stability — turns out to be uninvolved. The kinetic barrier is topological. It exists because of the knot's geometric relationship to the unfolding pathway, not because of any energetic preference for the folded state. Remove the thermodynamic explanation, and the prediction remains. In the plasticity case, the operative structure is the geometry of the quasilocalized excitations. Energy minimization — the physical principle that was presumed to generate the landscape — turns out to be unnecessary. The force geometry alone carries the prediction. Remove the conservative framework, and the prediction remains. The shared principle: when a prediction works across a domain boundary — from equilibrium to far-from-equilibrium (plasticity), from thermodynamic to purely kinetic (proteins) — the surviving element identifies the load-bearing variable. What survives is geometry. What falls away is the specific physical principle that generated the geometry in the original context. The energy landscape was not the prediction. It was a particular instantiation of the prediction. The geometry was the prediction all along.