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arXiv · 2512.21281

Hamilton-Jacobi as model reduction, extension to Newtonian particle mechanics, and a wave mechanical curiosity

Amit Acharya
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Abstract

The Hamilton-Jacobi equation of classical mechanics is approached as a model reduction of conservative particle mechanics where the velocity degrees-of-freedom are eliminated. This viewpoint allows an extension of the association of the Hamilton-Jacobi equation from conservative systems to general Newtonian particle systems involving non-conservative forces, including dissipative ones. A geometric optics approximation leads to a dissipative Schr\"odinger equation, with the expected limiting form when the associated classical force system involves conservative forces.

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Amit Acharya. 2025-12-24. Hamilton-Jacobi as model reduction, extension to Newtonian particle mechanics, and a wave mechanical curiosity. https://arxiv.org/abs/2512.21281

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