Thermodynamic Invariants of Coupled Channels: A Many-Channel Tolman-Ehrenfest Effect
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| Format: | Preprint |
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2026
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| _version_ | 1866917499328528384 |
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| author | Hamblin, Benjamin Calo, Victor Regenauer-Lieb, Klaus |
| author_facet | Hamblin, Benjamin Calo, Victor Regenauer-Lieb, Klaus |
| contents | When multiple thermodynamic channels are coupled, single-channel equilibrium conditions fail. Extending the Tolman--Ehrenfest effect to the entropy manifold, we derive the unique $n$-channel invariant $ζ_i T_i = C$, where $ζ_i$ is the holonomy of the Ruppeiner connection. For the granular volume--stress ensemble, Rowe's dilatancy ratio and energy restriction emerge as geometric consequences of the off-diagonal curvature $g_{Vσ}$, and the 60-year puzzle of state-dependent $K_μ$ is resolved: the correction $ζ_V$ reaches $O(1)$ near jamming. The prediction $ζ_Vχ=\mathrm{const}$ across a shear band is experimentally testable. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_15653 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Thermodynamic Invariants of Coupled Channels: A Many-Channel Tolman-Ehrenfest Effect Hamblin, Benjamin Calo, Victor Regenauer-Lieb, Klaus Mathematical Physics Materials Science Statistical Mechanics When multiple thermodynamic channels are coupled, single-channel equilibrium conditions fail. Extending the Tolman--Ehrenfest effect to the entropy manifold, we derive the unique $n$-channel invariant $ζ_i T_i = C$, where $ζ_i$ is the holonomy of the Ruppeiner connection. For the granular volume--stress ensemble, Rowe's dilatancy ratio and energy restriction emerge as geometric consequences of the off-diagonal curvature $g_{Vσ}$, and the 60-year puzzle of state-dependent $K_μ$ is resolved: the correction $ζ_V$ reaches $O(1)$ near jamming. The prediction $ζ_Vχ=\mathrm{const}$ across a shear band is experimentally testable. |
| title | Thermodynamic Invariants of Coupled Channels: A Many-Channel Tolman-Ehrenfest Effect |
| topic | Mathematical Physics Materials Science Statistical Mechanics |
| url | https://arxiv.org/abs/2605.15653 |