Multiscale Violation of Onsager Reciprocity: Thermomechanical Proof, Atomic Evidence, and Graphene Predictions

TL;DR

This paper introduces a geometric framework revealing multiscale violations of Onsager reciprocity, supported by atomic-scale evidence and graphene experiments, unifying microscopic irreversibility with macroscopic hysteresis.

Contribution

It develops a geometric approach to explain effective asymmetry in thermodynamic couplings, supported by microscopic theorems, atomic analysis, and experimental graphene data.

Findings

Atomic cross-derivative asymmetries peak at transition series anomalies.

Graphene exhibits statistically significant hysteresis loops.

The framework unifies microscopic irreversibility with macroscopic thermodynamic behavior.

Abstract

Onsager reciprocity $L_{ij}=L_{ji}$ is a cornerstone of near-equilibrium thermodynamics derived from microscopic time-reversal symmetry. We develop a geometric framework in which entropy-weighted reparameterization of thermodynamic response functions leads to an effective asymmetry in cross-couplings without violating the microscopic Onsager theorem. Motivated by the parallel structure of heat capacities $C_p$ and $C_v$, we introduce entropy-weighted response variables $\lambda_p$, $\lambda_v$, $\lambda_s$, and $\lambda_t$. Their ratios $\Gamma_c=\lambda_p/\lambda_v=C_v/C_p$ and $\Gamma_m=\lambda_s/\lambda_t=\kappa_T/\kappa_S$ form thermodynamic invariants whose product equals unity in equilibrium. Within a differential-form representation of thermodynamic state space, equilibrium corresponds to exactness of the accessibility form $\omega=\lambda_p\,dp+\lambda_v\,dv$ with $d\omega=0$, while non-equilibrium processes generate curvature $\Omega=d\omega$, producing an effective asymmetry in the transformed coupling matrix. A microscopic theorem shows that entropy-weighted statistical ensembles with time-reversal asymmetry $\chi(\Gamma)=W(\Theta\Gamma)/W(\Gamma)\neq1$ generate an antisymmetric contribution to the Green--Kubo transport matrix. Atomic-scale analysis using the Transforma model reveals cross-derivative asymmetries across the $3d$ transition series, peaking at configuration anomalies in Cr and Cu. Temperature-dependent Raman spectroscopy of monolayer graphene exhibits statistically significant hysteresis loops (up to $30\sigma$), providing experimental evidence for thermodynamic curvature. These results unify microscopic irreversibility, atomic structure anomalies, and macroscopic hysteresis within a geometric interpretation of entropy-weighted thermodynamic coupling.