| _version_ | 1866901772888440832 |
|---|---|
| author | SCHORR, RICHARD |
| author_facet | SCHORR, RICHARD |
| contents | <p>Every electrical generator in existence operates by one mechanism: forcing carriers across field gradients.<br>Those gradient fields are everywhere -- thermal, electromagnetic, kinetic, chemical. The Phase-Modulated<br>Information Rivalry (PMIR) framework, previously validated across brain connectomes, financial networks,<br>and climate systems with r = 0.9852 [1], identifies the algebraic connectivity λ<br>2<br> of a system's graph Laplacian<br>as the universal regime-transition parameter. Here we apply this framework to energy conversion efficiency,<br>proposing that the Mott formula for thermoelectric Seebeck coefficient is a λ<br>2<br> spectral gradient expression,<br>and that optimal thermoelectric figure of merit ZT is reached near the non-degenerate/degenerate transport<br>crossover -- the λ<br>2<br> transition of the electron hopping graph. Single-band model calculations confirm ZT peaks<br>at reduced Fermi energy eta = -0.30 (near the transition at eta = 0), with Seebeck coefficient 224 microV/K vs<br>published 200 microV/K (12% gap), consistent with Snyder and Toberer's empirical finding that optimal ZT<br>occurs at the semiconducting-to-metallic transition [6]. Photovoltaic efficiency limits (Shockley-Queisser)<br>provide an honest null result: these are source-spectrum determined and do not correspond to any material<br>phase transition. PMIR provides both a theoretical language for existing empirical observations and a<br>community-executable prediction via the Materials Project database.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20213031 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Hidden in the Phase Transition: Spectral Graph Theory Unifies Optimal Operating Points in Energy Conversion Efficiency SCHORR, RICHARD <p>Every electrical generator in existence operates by one mechanism: forcing carriers across field gradients.<br>Those gradient fields are everywhere -- thermal, electromagnetic, kinetic, chemical. The Phase-Modulated<br>Information Rivalry (PMIR) framework, previously validated across brain connectomes, financial networks,<br>and climate systems with r = 0.9852 [1], identifies the algebraic connectivity λ<br>2<br> of a system's graph Laplacian<br>as the universal regime-transition parameter. Here we apply this framework to energy conversion efficiency,<br>proposing that the Mott formula for thermoelectric Seebeck coefficient is a λ<br>2<br> spectral gradient expression,<br>and that optimal thermoelectric figure of merit ZT is reached near the non-degenerate/degenerate transport<br>crossover -- the λ<br>2<br> transition of the electron hopping graph. Single-band model calculations confirm ZT peaks<br>at reduced Fermi energy eta = -0.30 (near the transition at eta = 0), with Seebeck coefficient 224 microV/K vs<br>published 200 microV/K (12% gap), consistent with Snyder and Toberer's empirical finding that optimal ZT<br>occurs at the semiconducting-to-metallic transition [6]. Photovoltaic efficiency limits (Shockley-Queisser)<br>provide an honest null result: these are source-spectrum determined and do not correspond to any material<br>phase transition. PMIR provides both a theoretical language for existing empirical observations and a<br>community-executable prediction via the Materials Project database.</p> |
| title | Hidden in the Phase Transition: Spectral Graph Theory Unifies Optimal Operating Points in Energy Conversion Efficiency |
| url | https://doi.org/10.5281/zenodo.20213031 |