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What is the most optimal diffusion?
Vasili Baranau
https://arxiv.org/abs/2510.07571 https://arxiv.org/pdf/2510.07571

What is the most optimal diffusion?
What is the fastest possible "diffusion"? A trivial answer would be "a process that converts a Dirac delta-function into a uniform distribution infinitely fast". Below, we consider a more reasonable formulation: a process that maximizes differential entropy of a probability density function (pdf) $f(\vec{x}, t)$ at every time $t$, under certain restrictions. Specifically, we focus on a case when the rate of the Kullback-Leibler divergence $D_{\text{KL}}$ is fixed. If $Δ(\vec{x}, t, d{t}) = \fr…

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