Assuming that the free energy of a gas depends non-locally on the logarithm of its mass density, the body force in the resulting equation of motion consists of the sum of density gradient terms. Truncating this series after the second term, Bohm’s quantum potential and the Madelung equation are identically obtained, showing explicitly that some of the hypotheses that led to the formulation of quantum mechanics admit a classical interpretation based on non-locality.

中文翻译：

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玻姆量子势的非局部相场模型

假设气体的自由能非局部地取决于其质量密度的对数，则所产生的运动方程中的体力由密度梯度项的总和组成。在第二项之后截断该系列，可以完全获得Bohm的量子势和Madelung方程，这清楚地表明，导致量子力学公式化的某些假设承认了基于非局部性的经典解释。