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

Monty Dabas

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 $λ_p$, $λ_v$, $λ_s$, and $λ_t$. Their ratios $Γ_c=λ_p/λ_v=C_v/C_p$ and $Γ_m=λ_s/λ_t=κ_T/κ_S$ 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 $ω=λ_p\,dp+λ_v\,dv$ with $dω=0$, while non-equilibrium processes generate curvature $Ω=dω$, producing an effective asymmetry in the transformed coupling matrix. A microscopic theorem shows that entropy-weighted statistical ensembles with time-reversal asymmetry $χ(Γ)=W(ΘΓ)/W(Γ)\neq1$ 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 $30σ$), 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.

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

Abstract

Onsager reciprocity 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 and , we introduce entropy-weighted response variables , , , and . Their ratios and 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 with , while non-equilibrium processes generate curvature , producing an effective asymmetry in the transformed coupling matrix. A microscopic theorem shows that entropy-weighted statistical ensembles with time-reversal asymmetry generate an antisymmetric contribution to the Green--Kubo transport matrix. Atomic-scale analysis using the Transforma model reveals cross-derivative asymmetries across the transition series, peaking at configuration anomalies in Cr and Cu. Temperature-dependent Raman spectroscopy of monolayer graphene exhibits statistically significant hysteresis loops (up to ), 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.
Paper Structure (52 sections, 4 theorems, 39 equations, 13 figures, 6 tables)

This paper contains 52 sections, 4 theorems, 39 equations, 13 figures, 6 tables.

Table of Contents

  1. Geometric Foundation: The TVSP Compass
  2. Example: T-V Quadrant.
  3. Entropy-Weighted Thermodynamic Coupling
  4. State function verification.
  5. Important disclaimer.
  6. Thermodynamic Invariants
  7. Equilibrium constraint.
  8. Experimental accessibility.
  9. Geometric Interpretation: Curvature as the Fundamental Object
  10. Equilibrium: exactness.
  11. Non-equilibrium: curvature.
  12. Stokes' theorem and hysteresis.
  13. Microscopic Foundation: Irreversibility from Weighted Ensembles
  14. Microscopic Setup and Weighted Ensemble
  15. Weighted Green--Kubo Transport Matrix
  16. ...and 37 more sections

Key Result

Theorem 5.1

For a system with time-reversal covariant microscopic dynamics and weighting factor $\chi(\Gamma)$ as defined above, the weighted transport coefficients satisfy

Figures (13)

  • Figure 1: Predicted entropy hysteresis loop as a function of temperature showing heating and cooling branches.
  • Figure 2: Predicted temperature dependence of the parameter $\Gamma^{*}(T)$.
  • Figure 3: Temperature dependence of coupling parameters $\lambda_p$ and $\lambda_v$.
  • Figure 4: Predicted quantum coherence time $T_2$ as a function of temperature.
  • Figure 5: Regularized temperature dependence of $\Gamma^{*}_{reg}(T)$.
  • ...and 8 more figures

Theorems & Definitions (5)

  • Theorem 5.1: Weighted Reciprocity
  • proof
  • Corollary 5.1.1: Classical Onsager Recovery
  • Corollary 5.1.2: Generic Irreversibility
  • Theorem 5.2: Microscopic Irreversibility