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arXiv · 2608.13894

de Broglie-Bohm Dynamics with Schr\"odinger Source Fields: A Framework for Subquantum Theory

Said Mikki
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Abstract

We extend de Broglie--Bohm (dBB) pilot-wave theory by introducing a complex source field into the Schr\"odinger equation and examining its effects on quantum equilibrium and nonequilibrium dynamics. In dBB theory, the physical particle distribution P, rather than the Born density $|{\psi}|^2$, carries the ensemble probability, so a source term may modify the pilot wave without violating conservation of total particle probability. We derive the source-modified Hamilton--Jacobi and continuity equations, the transport equation for the nonequilibrium ratio $f=P/|{\psi}|^2$, and an exact entropy-production formula. Three applications follow. First, suitably designed sources can drive exponential relaxation toward quantum equilibrium. Second, the entropy-production rate admits a Prigogine-type bilinear form, providing a basis for a subquantum thermodynamics with entropy-producing and entropy-extracting regimes. Third, a tuned source can exactly cancel the Bohmian quantum potential, yielding classical particle trajectories while the guiding wave retains nontrivial structure and the nonequilibrium ratio remains conserved. The resulting framework provides a unified setting for studying source-driven quantum nonequilibrium, entropy exchange, and classicalization, and motivates further investigation of the physical and ontological status of the source field.

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Said Mikki. 2026-08-14. de Broglie-Bohm Dynamics with Schr\"odinger Source Fields: A Framework for Subquantum Theory. https://arxiv.org/abs/2608.13894

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