{
  "id": "oai:papers.qnfo.org:reynolds-filter-and-the-observability-of-chaos",
  "slug": "reynolds-filter-and-the-observability-of-chaos",
  "title": "REYNOLDS FILTER AND THE OBSERVABILITY OF CHAOS",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "The transition to turbulence is characterized by universal scaling laws, specifically the Feigenbaum constants, which govern the onset of chaos in nonlinear systems. While these constants are traditionally viewed as topological invariants of the underlying dynamical maps, their observability in macroscopic physical systems is strictly conditioned by the separation of scales between the dynamics and the observer. We investigate this conditioning by simulating a stochastic Rössler system subject to a “Reynolds Filter,” a temporal averaging functional that mimics the coarse-graining inherent in thermodynamic observation. We demonstrate that the “onset of chaos” perceived by a macroscopic observer corresponds to the spectral leakage of subharmonic frequencies through the filter’s stopband. We show that the variance of the filtered macroscopic variable acts as a robust order parameter, exhibiting scaling behavior consistent with α² at bifurcation points. [...]",
  "abstract_markdown": "The transition to turbulence is characterized by universal scaling laws, specifically the Feigenbaum constants, which govern the onset of chaos in nonlinear systems. While these constants are traditionally viewed as topological invariants of the underlying dynamical maps, their observability in macroscopic physical systems is strictly conditioned by the separation of scales between the dynamics and the observer. We investigate this conditioning by simulating a stochastic Rössler system subject to a “Reynolds Filter,” a temporal averaging functional that mimics the coarse-graining inherent in thermodynamic observation. We demonstrate that the “onset of chaos” perceived by a macroscopic observer corresponds to the spectral leakage of subharmonic frequencies through the filter’s stopband. We show that the variance of the filtered macroscopic variable acts as a robust order parameter, exhibiting scaling behavior consistent with \\(\\alpha^2\\) at bifurcation points. [...]",
  "date": "2025-12-01",
  "first_published": "2025-12-01",
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  "url": "https://papers.qnfo.org/papers/reynolds-filter-and-the-observability-of-chaos",
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        "name": "Rowan Brad Quni-Gudzinas",
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    "titles": [
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        "title": "REYNOLDS FILTER AND THE OBSERVABILITY OF CHAOS"
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        "description": "The transition to turbulence is characterized by universal scaling laws, specifically the Feigenbaum constants, which govern the onset of chaos in nonlinear systems. While these constants are traditionally viewed as topological invariants of the underlying dynamical maps, their observability in macroscopic physical systems is strictly conditioned by the separation of scales between the dynamics and the observer. We investigate this conditioning by simulating a stochastic Rössler system subject to a “Reynolds Filter,” a temporal averaging functional that mimics the coarse-graining inherent in thermodynamic observation. We demonstrate that the “onset of chaos” perceived by a macroscopic observer corresponds to the spectral leakage of subharmonic frequencies through the filter’s stopband. We show that the variance of the filtered macroscopic variable acts as a robust order parameter, exhibiting scaling behavior consistent with α² at bifurcation points. [...]",
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