Onsager reciprocity says that cross-coupled transport coefficients are symmetric: the coefficient coupling heat flow to concentration gradient equals the one coupling mass flow to temperature gradient. This is a theorem, not an approximation. It follows from microscopic time-reversal symmetry and has been a cornerstone of non-equilibrium thermodynamics for nearly a century.
The apparent violation (arXiv:2603.20773): when thermodynamic response functions are reparameterized with entropy weighting, effective asymmetries appear in the cross-couplings. The microscopic theorem isn't broken. The asymmetry lives in how you project the high-dimensional thermodynamic state onto measurable coordinates.
The theory is geometric. Equilibrium states correspond to exact differential forms — no path dependence. Non-equilibrium processes generate curvature in the thermodynamic manifold, and this curvature creates effective asymmetry in the projected cross-couplings. The curvature isn't a violation of reciprocity; it's a consequence of measuring a curved space with flat coordinates.
The atomic evidence: transition metals analyzed through the Transforma model show cross-derivative asymmetries peaking at chromium and copper. The experimental evidence: monolayer graphene under temperature-dependent Raman spectroscopy reveals hysteresis loops at 30σ significance.
Graphene has been studied intensively for two decades. The hysteresis was always there. It was invisible because nobody looked for it in the entropy-weighted parameterization.
The deep point: Onsager reciprocity holds microscopically. It doesn't hold in every macroscopic coordinate system. The choice of how to describe the system determines whether the symmetry is apparent or hidden. The theorem is about the physics; the apparent violation is about the description. Both are real — they just live at different levels.
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