Paper
Precision's arrow of time
Authors
Luis E. F. Foa Torres, G. Pappas, V. Achilleos, D. Bautista Avilés
Abstract
The arrow of time is usually attributed to two mechanisms: decoherence through environmental entanglement, and chaos through nonlinear dynamics. Here we demonstrate a third route, Precision-Induced Irreversibility (PIR), requiring neither. No entanglement. No nonlinearity. Just three ingredients: amplification, non-normality, and finite dynamic range, whose interplay yields an operational arrow of time; remove any one and reversibility can be restored. Non-Hermitian evolution remains mathematically invertible, yet beyond a sharp temporal predictability horizon scaling linearly with available precision, distinct states collapse onto identical representations. Echo-fidelity tests confirm this transition across arbitrary-precision calculations and hardware, revealing where formal invertibility and physical reversibility diverge.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.22284v1</id>\n <title>Precision's arrow of time</title>\n <updated>2026-03-23T17:59:50Z</updated>\n <link href='https://arxiv.org/abs/2603.22284v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.22284v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>The arrow of time is usually attributed to two mechanisms: decoherence through environmental entanglement, and chaos through nonlinear dynamics. Here we demonstrate a third route, Precision-Induced Irreversibility (PIR), requiring neither. No entanglement. No nonlinearity. Just three ingredients: amplification, non-normality, and finite dynamic range, whose interplay yields an operational arrow of time; remove any one and reversibility can be restored. Non-Hermitian evolution remains mathematically invertible, yet beyond a sharp temporal predictability horizon scaling linearly with available precision, distinct states collapse onto identical representations. Echo-fidelity tests confirm this transition across arbitrary-precision calculations and hardware, revealing where formal invertibility and physical reversibility diverge.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='quant-ph'/>\n <category scheme='http://arxiv.org/schemas/atom' term='cond-mat.stat-mech'/>\n <published>2026-03-23T17:59:50Z</published>\n <arxiv:comment>5 pages, 3 figures; includes Supplemental Material (17 pages, 3 figures)</arxiv:comment>\n <arxiv:primary_category term='quant-ph'/>\n <author>\n <name>Luis E. F. Foa Torres</name>\n </author>\n <author>\n <name>G. Pappas</name>\n </author>\n <author>\n <name>V. Achilleos</name>\n </author>\n <author>\n <name>D. Bautista Avilés</name>\n </author>\n </entry>"
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