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  "body": "\n## Summary\n\nThe Jordan–Kinderlehrer–Otto scheme, or JKO scheme, is a time discretization of a gradient flow in the space of probability measures with the [[Wasserstein distance|VEY29CS26X]].\nAt each step it minimizes the energy plus a penalty for moving far, in Wasserstein distance, from the previous measure.\nRichard Jordan, David Kinderlehrer and Felix Otto introduced it in 1998 and proved that it converges to solutions of the [[Fokker–Planck equation|FVQWR7NS00]].\nIt showed that the [[heat equation|VP2HN86VAG]] is the gradient flow of the entropy for the Wasserstein distance, and started the theory of Wasserstein gradient flows.\n\n## Explanations\n\n### L1 human\n\nImagine a drop of ink spreading in water.\nThe JKO scheme describes this spreading in small time steps.\nAt each step, the ink chooses a new distribution that lowers its energy, an entropy term that favours spreading out.\nIt also pays a cost for how far its mass has to travel.\nWhen the steps become very short, the result is the heat equation, so diffusion is a way of decreasing entropy as fast as possible for the cost of moving mass.\n",
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