Weakly non-local fluid mechanics: The Schrödinger equation

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11 Citations (Scopus)


A weakly non-local extension of ideal fluid dynamics is derived from the Second Law of thermodynamics. It is proved that in the reversible limit, the additional pressure term can be derived from a potential. The requirement of the additivity of the specific entropy function determines the quantum potential uniquely. The relation to other known derivations of the Schrödinger equation (stochastic, Fisher information, exact uncertainty) is clarified.

Original languageEnglish
Pages (from-to)541-557
Number of pages17
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2066
Publication statusPublished - Jan 1 2006


  • Korteweg fluids
  • Liu procedure
  • Schrödinger equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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