Entropy-Weighted Thermodynamic Coupling and Raman Signatures of Non-Reciprocal Response in Graphene

Onsager reciprocity is a cornerstone of near-equilibrium thermodynamics, yet deviations may emerge when coupling between thermodynamic variables becomes strongly asymmetric. Here we develop a multiscale framework in which entropy-weighted thermoelastic interactions generate path-dependent responses that can be probed experimentally. An analytical derivation predicts asymmetric cross-derivative behaviour, supported by atomic-scale modelling that reveals non-reciprocal trends across electronic configurations. To test these ideas experimentally, we perform temperature-dependent Raman spectroscopy on monolayer graphene during controlled heating–cooling cycles. Measurements acquired at CeNSE under a calibrated experimental protocol show reproducible hysteresis in both the G and 2D phonon modes, indicating path-dependent phonon evolution. The agreement between theoretical expectations and spectroscopic observables suggests that entropy-mediated coupling can produce measurable non-reciprocal behaviour in two-dimensional materials. These results provide an experimentally accessible route to exploring thermodynamic asymmetry and may have implications for non-reciprocal thermal transport, quantum materials design and phonon-based information control.