On the Non-Preservability of Global Accessibility Invariants under Locally Admissible Transformations

Irreversibility is commonly analysed through instability, entropy production, or unpredictability. In this article, we establish a negative structural result concerning irreversible systems subject to locally admissible transformations. We show that, in a broad class of such systems, no global invariant capable of ensuring future accessibility can be preserved under the full set of transformations that locally preserve structure. This impossibility does not arise from noise, lack of regularity, or epistemic limitation, but from an incompatibility between local admissibility and the global structure of accessibility itself. The result extends classical limitations identified by Poincaré by shifting the obstruction from predictability to the non-preservability of global accessibility invariants. No explicit construction is provided, as the argument concerns a structural incompatibility rather than a particular dynamical instance.