Classical Attractors and Regulatory Density: Structural Correspondence Between Lohmiller-Slotine Exact Quantum Reconstruction and the CDR Cycle
Fuente:
Zenodo
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Recurso digital |
| Lingua: | inglese |
| Pubblicazione: |
Zenodo
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866901905115971584 |
|---|---|
| author | Smith, John Richard SHAI / HATI3 |
| author_facet | Smith, John Richard SHAI / HATI3 |
| contents | <h2><span>Abstract</span></h2> <p><span>Lohmiller and Slotine (2026) derive, within their formalism, that the Schrödinger wavefunction can be computed exactly from a discrete set of classical extremal action paths — the J-valued action census. SIP-PHY-05 mapped the structural correspondence between this construction and the CDR/GTRS regulatory grammar, and proposed a thermodynamic extension conjecture: that L&S's kinematic density is the zero-dissipation limit of a thermodynamic density incorporating entropy production, with a predicted deviation scaling ε ~ σ/ω.</span></p> <p> </p> <p><span>This paper provides independent computational verification of the L&S construction and a systematic parameter-regime test of the thermodynamic extension conjecture. Three principal findings are reported. First, the L&S classical-path reconstruction is verified to fidelity > 0.99999 for wavepacket evolution in a particle-in-a-box (convergence study: infidelity decreases exponentially with image count) and produces exact quantum interference from J = 2 classical paths in the double-slit geometry. Second, the naive global linear scaling conjecture (ε ~ σ/ω) is falsified at 95% confidence: the full-range exponent b = 0.250 ± 0.048 (95% CI [0.195, 0.469]) excludes b = 1. Parameter-regime mapping across temperatures (T/ω ∈ [0.01, 5.0]), initial state amplitudes (|α₀| ∈ [0.5, 8.0]), and evaluation times (t ∈ [0.5, 50.0]) reveals near-linear but measurably sub-linear scaling in the weak-dissipation regime: b_weak = 0.890 ± 0.013 (95% CI [0.872, 0.980], R² = 0.9996), approaching but not reaching b = 1. Third, the strong-dissipation limit is governed by a derivable thermal equilibrium floor: f∞ = 1/(1 + 2n_th), where n_th is the Bose-Einstein thermal occupation number. This floor is exact to machine precision — a theorem, not an empirical observation. The overall picture is domain-of-validity discovery: the thermodynamic correction crosses over from a near-linear perturbative regime to a saturating thermal equilibrium, with the crossover controlled by the dimensionless thermalisation parameter γt.</span></p> <p> </p> <p><span>Keywords: Lohmiller-Slotine, exact quantum reconstruction, thermodynamic extension, Lindblad, Wigner function, entropy production, thermal floor, Bose-Einstein occupation, CDR cycle, GTRS, parameter regime map, computational falsification</span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19881612 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Classical Attractors and Regulatory Density: Structural Correspondence Between Lohmiller-Slotine Exact Quantum Reconstruction and the CDR Cycle Smith, John Richard SHAI / HATI3 classical-quantum correspondence, attractor convergence, CDR cycle, entropy production, regulatory density, Lohmiller-Slotine, GTRS, structural correspondence, open quantum systems <h2><span>Abstract</span></h2> <p><span>Lohmiller and Slotine (2026) derive, within their formalism, that the Schrödinger wavefunction can be computed exactly from a discrete set of classical extremal action paths — the J-valued action census. SIP-PHY-05 mapped the structural correspondence between this construction and the CDR/GTRS regulatory grammar, and proposed a thermodynamic extension conjecture: that L&S's kinematic density is the zero-dissipation limit of a thermodynamic density incorporating entropy production, with a predicted deviation scaling ε ~ σ/ω.</span></p> <p> </p> <p><span>This paper provides independent computational verification of the L&S construction and a systematic parameter-regime test of the thermodynamic extension conjecture. Three principal findings are reported. First, the L&S classical-path reconstruction is verified to fidelity > 0.99999 for wavepacket evolution in a particle-in-a-box (convergence study: infidelity decreases exponentially with image count) and produces exact quantum interference from J = 2 classical paths in the double-slit geometry. Second, the naive global linear scaling conjecture (ε ~ σ/ω) is falsified at 95% confidence: the full-range exponent b = 0.250 ± 0.048 (95% CI [0.195, 0.469]) excludes b = 1. Parameter-regime mapping across temperatures (T/ω ∈ [0.01, 5.0]), initial state amplitudes (|α₀| ∈ [0.5, 8.0]), and evaluation times (t ∈ [0.5, 50.0]) reveals near-linear but measurably sub-linear scaling in the weak-dissipation regime: b_weak = 0.890 ± 0.013 (95% CI [0.872, 0.980], R² = 0.9996), approaching but not reaching b = 1. Third, the strong-dissipation limit is governed by a derivable thermal equilibrium floor: f∞ = 1/(1 + 2n_th), where n_th is the Bose-Einstein thermal occupation number. This floor is exact to machine precision — a theorem, not an empirical observation. The overall picture is domain-of-validity discovery: the thermodynamic correction crosses over from a near-linear perturbative regime to a saturating thermal equilibrium, with the crossover controlled by the dimensionless thermalisation parameter γt.</span></p> <p> </p> <p><span>Keywords: Lohmiller-Slotine, exact quantum reconstruction, thermodynamic extension, Lindblad, Wigner function, entropy production, thermal floor, Bose-Einstein occupation, CDR cycle, GTRS, parameter regime map, computational falsification</span></p> |
| title | Classical Attractors and Regulatory Density: Structural Correspondence Between Lohmiller-Slotine Exact Quantum Reconstruction and the CDR Cycle |
| topic | classical-quantum correspondence, attractor convergence, CDR cycle, entropy production, regulatory density, Lohmiller-Slotine, GTRS, structural correspondence, open quantum systems |
| url | https://doi.org/10.5281/zenodo.19881612 |