On Entropy Production in the Madelung Fluid and the Role of Bohm’s Potential in Classical Diffusion

  title={On Entropy Production in the Madelung Fluid and the Role of Bohm’s Potential in Classical Diffusion},
  author={Eyal Heifetz and Roumen Tsekov and Eliahu Cohen and Zohar Nussinov},
  journal={Foundations of Physics},
The Madelung equations map the non-relativistic time-dependent Schrödinger equation into hydrodynamic equations of a virtual fluid. While the von Neumann entropy remains constant, we demonstrate that an increase of the Shannon entropy, associated with this Madelung fluid, is proportional to the expectation value of its velocity divergence. Hence, the Shannon entropy may grow (or decrease) due to an expansion (or compression) of the Madelung fluid. These effects result from the interference… 
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The author acknowledges helpful discussions with R. Barankov on earlier stages of this work. The author also thanks C. Gogolin for sharing the proof of Eq. (24) and for many valuable comments. It is