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Line 1: − '''Mathematical entropy''' is a formulation of [[entropy]] for mathematical purposes, particularly in geometry. A definition of entropy by Perelman, for example, led to his solution of one of the greatest unsolved problems of the 20th century, the Poincare conjecture. − + − A related concept is the "Nash entropy."+ + +
Mathematical entropy (view source)
Revision as of 08:33, December 22, 2009
, 08:33, December 22, 2009no edit summary
{{merge|Poincaré conjecture#Perelman's Proof}}
{{merge|Poincaré conjecture#Perelman's Proof}}
Perelman's formulation of entropy is useful in addressing issues in mechanical engineering, and in particular the linear heat equation.<ref>http://math.ucsd.edu/~lni/academic/ni_add.pdf</ref>
In mathematics, particuarly in geometry and differential equations, several phenomenon appear which behave similarly to entropy in physics. 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 is useful in addressing issues in mechanical engineering, and in particular the linear heat equation.<ref>http://math.ucsd.edu/~lni/academic/ni_add.pdf</ref>
Nash entropy is a concept in game theory which behaves similarly to entropy in statistical mechanics.
== References ==
== References ==