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Mathematical entropy (view source)

Revision as of 17:57, December 23, 2009

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Ricci flow, used by Perelman for his solution of one of the greatest unsolved problems of the 20th century, the [[Poincare conjecture]], behaves similarly to heat dispersion, which is a form of entropy.

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Noticing this (and other similarities between the effect of Ricci flow on a manifolds metric and the effect of time on heat dispersion, Perelman formulated the concept of "Perelman entropy."

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Noticing this (and other similarities between the effect of Ricci flow on a manifolds metric and the effect of time on heat dispersion), Perelman formulated the concept of "Perelman entropy." By focusing on entropy, Perelman unlocked and solved one of the greatest mathematical mysteries of the 20th century.

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Perelman's insight was to develop and use an estimate for entropy such that "a special eigenvalue of the manifold undergoing the Ricci flow and cut/paste process is increasing."<ref>http://comet.lehman.cuny.edu/sormani/others/perelman/introperelman.html</ref>

==Nash Entropy==

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