Difference between revisions of "Mathematical entropy"
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| − | + | In mathematics, particularly in geometry and differential equations, several phenomenon appear which behave similarly to entropy in physics. | |
| − | + | ==Perelman Entropy== | |
| + | ::''For more on this subject, see [[Poincaré conjecture#Perelman's Proof|Perelman's proof of the Poincaré conjecture]].'' | ||
| + | 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. | ||
| − | Ricci flow | + | 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." |
| + | ==Nash Entropy== | ||
Nash entropy is a concept in game theory which behaves similarly to entropy in statistical mechanics. | Nash entropy is a concept in game theory which behaves similarly to entropy in statistical mechanics. | ||
| + | ==Entropy in Engineering== | ||
Mathematical entropy is useful in solving shallow water equations. | Mathematical entropy is useful in solving shallow water equations. | ||
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[[Category:mathematics]] | [[Category:mathematics]] | ||
Revision as of 09:20, December 23, 2009
In mathematics, particularly in geometry and differential equations, several phenomenon appear which behave similarly to entropy in physics.
Perelman Entropy
- For more on this subject, see Perelman's proof of the Poincaré conjecture.
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.
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."
Nash Entropy
Nash entropy is a concept in game theory which behaves similarly to entropy in statistical mechanics.
Entropy in Engineering
Mathematical entropy is useful in solving shallow water equations.