Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Recurso digital |
| Langue: | anglais |
| Publié: |
Zenodo
2026
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| Sujets: | |
| Accès en ligne: | https://doi.org/10.5281/zenodo.18126306 |
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- <p>This upload contains an 8-page note introducing <strong>Equivariant Window Embeddings (EWE)</strong>: a model-independent, symmetry-based diagnostic for detecting <strong>broken time-reversal symmetry / failure of detailed balance</strong> from <strong>finite trajectory data</strong>. The method maps two-sided trajectory windows into a feature space via an equivariant embedding <span><span>Φ\Phi</span><span><span><span>Φ</span></span></span></span> that commutes with time reversal, <span><span>Φ(Rω)=JΦ(ω)\Phi(R\omega)=J\Phi(\omega)</span><span><span><span>Φ</span><span>(</span><span>R</span><span>ω</span><span>)</span><span>=</span></span><span><span>J</span><span>Φ</span><span>(</span><span>ω</span><span>)</span></span></span></span>, and evaluates an observable <span><span>GG</span><span><span><span>G</span></span></span></span> that is odd under the induced involution, <span><span>G(Jv)=−G(v)G(Jv)=-G(v)</span><span><span><span>G</span><span>(</span><span>J</span><span>v</span><span>)</span><span>=</span></span><span><span>−</span><span>G</span><span>(</span><span>v</span><span>)</span></span></span></span>. The core result (Theorem 3.1) shows that under detailed balance the expectation <span><span>E[G(Φ(ω))]\mathbb{E}[G(\Phi(\omega))]</span><span><span><span>E</span><span>[</span><span>G</span><span>(</span><span>Φ</span><span>(</span><span>ω</span><span>))]</span></span></span></span> must vanish; therefore a statistically significant nonzero empirical mean provides a <strong>certificate of irreversibility</strong> and (in physical settings) <strong>nonzero entropy production</strong> without fitting parametric models or estimating forward–reverse likelihood ratios.</p>