Delayed Arrow-of-Time Detection in Signed Laplacian Dynamics
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911006977949696 |
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| author | Brandenburger, Adam La Mura, Pierfrancesco |
| author_facet | Brandenburger, Adam La Mura, Pierfrancesco |
| contents | We study how rapidly the direction of time becomes operationally detectable from mesoscopic data when state-weights may be positive or negative. In contrast with classical Markov processes -- where forward evolution is instantly distinguishable from its reverse -- signed dynamics can render the arrow of time undetectable during an initial interval. Assume the generator of the signed dynamics is a symmetric signed Laplacian with a single linear invariant and a phase-space Second Law holds in the form of non-decreasing Rényi-$2$ entropy. Drawing on recent results on eventual exponential positivity of signed Laplacians (Chen et al., 2021), we define a test that correctly identifies the direction of thermodynamic time if conducted over a time interval of length at least $τ$. We go on to prove that the test cannot deliver an incorrect conclusion if conducted over a shorter interval. Dropping symmetry, we exhibit a superquantum example where $τ= +\infty$, so that the arrow of time remains permanently undetectable under our test. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08236 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Delayed Arrow-of-Time Detection in Signed Laplacian Dynamics Brandenburger, Adam La Mura, Pierfrancesco Quantum Physics Mathematical Physics We study how rapidly the direction of time becomes operationally detectable from mesoscopic data when state-weights may be positive or negative. In contrast with classical Markov processes -- where forward evolution is instantly distinguishable from its reverse -- signed dynamics can render the arrow of time undetectable during an initial interval. Assume the generator of the signed dynamics is a symmetric signed Laplacian with a single linear invariant and a phase-space Second Law holds in the form of non-decreasing Rényi-$2$ entropy. Drawing on recent results on eventual exponential positivity of signed Laplacians (Chen et al., 2021), we define a test that correctly identifies the direction of thermodynamic time if conducted over a time interval of length at least $τ$. We go on to prove that the test cannot deliver an incorrect conclusion if conducted over a shorter interval. Dropping symmetry, we exhibit a superquantum example where $τ= +\infty$, so that the arrow of time remains permanently undetectable under our test. |
| title | Delayed Arrow-of-Time Detection in Signed Laplacian Dynamics |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2506.08236 |