Dissipative Hamilton Jacobi Dynamics and the Emergence of Quantum Wave Mechanics

Quantum Physics [Submitted on 7 Apr 2026] Dissipative Hamilton Jacobi Dynamics and the Emergence of Quantum Wave Mechanics Naleli Jubert Matjelo We develop a dissipative extension of classical mechanics based on a complex, and more generally quaternionic, action principle that endows every classical system with an intrinsic environment. Decomposing the action into conservative and divergence-induced components yields two coupled Hamilton Jacobi equations describing a dynamically intertwined system environment pair. This motivates a Dual Sector or Dual Environmental Interpretation (DSI/DEI), in which the additional degrees of freedom behave as an image sector exchanging energy, information, and phase with the system. Applying a generalized Madelung transform produces a nonlinear dissipative wave equation whose symmetric equilibrium limit reduces to the Schroedinger equation, with the quantum potential and linearity emerging from balanced intersector coupling. In this framework, the wavefunction is not fundamental but encodes the interaction geometry between system and environment, providing a classical origin for interference, amplitude phase coupling, and probabilistic structure. Extending the imaginary structure to multiple independent directions yields a multienvironment generalization capable of representing measurement-like processes, nonMarkovian memory, and entanglement type correlations. The formulation unifies aspects of dual-system models, hydrodynamic approaches, and non-Hermitian dynamics within a single action-based framework, and suggests that quantum mechanics corresponds to a stable symmetric phase of a broader dissipative classical theory. Comments: 17 pages, 0 figures, not submitted for publishing Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.06455 [quant-ph]   (or arXiv:2604.06455v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.06455 Focus to learn more Submission history From: Naleli Matjelo Dr [view email] [v1] Tue, 7 Apr 2026 20:53:38 UTC (23 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)