AI 中文总结
该研究扩展德布罗意-玻姆导波理论，引入薛定谔源场推导相关方程，其应用可驱动量子平衡弛豫、构建亚量子热力学、抵消玻姆量子势，为相关研究提供统一框架。
AI 中文摘要
我们通过在薛定谔方程中引入复源场并研究其对量子平衡与非平衡动力学的影响，扩展了德布罗意-玻姆（dBB）导波理论。在dBB理论中，物理粒子分布P（而非玻恩密度|ψ|²）携带系综概率，因此源项可修改导波且不违背总粒子概率守恒。我们推导了源修正的哈密顿-雅可比方程与连续性方程、非平衡比f=P/|ψ|²的输运方程，以及精确的熵产生公式。随后给出三项应用：其一，适当设计的源可驱动指数弛豫至量子平衡；其二，熵产生率具有普里戈金型双线性形式，为含熵产生与熵提取 regime 的亚量子热力学提供基础；其三，调谐后的源可精确抵消玻姆量子势，产生经典粒子轨迹，同时导波保留非平凡结构且非平衡比保持守恒。所得框架为研究源驱动的量子非平衡、熵交换与经典化提供统一场景，并推动进一步探究源场的物理与本体论地位。
英文摘要
We extend de Broglie--Bohm (dBB) pilot-wave theory by introducing a complex source field into the Schrödinger equation and examining its effects on quantum equilibrium and nonequilibrium dynamics. In dBB theory, the physical particle distribution P, rather than the Born density $|ψ|^2$, 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 $f=P/|ψ|^2$, 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.
