Extremal flows in Wasserstein space

Giovanni Conforti, Michele Pavon

Research output: Contribution to journalArticlepeer-review


We develop an intrinsic geometric approach to the calculus of variations in the Wasserstein space. We show that the flows associated with the Schrödinger bridge with general prior, with optimal mass transport, and with the Madelung fluid can all be characterized as annihilating the first variation of a suitable action. We then discuss the implications of this unified framework for stochastic mechanics: It entails, in particular, a sort of fluid-dynamic reconciliation between Bohm's and Nelson's stochastic mechanics.

Original languageEnglish (US)
Article number063502
JournalJournal of Mathematical Physics
Issue number6
StatePublished - Jun 1 2018

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


Dive into the research topics of 'Extremal flows in Wasserstein space'. Together they form a unique fingerprint.

Cite this