Mathematical entropy
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In mathematics, particularly 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.[1]
Nash entropy is a concept in game theory which behaves similarly to entropy in statistical mechanics.
Mathematical entropy is useful in solving shallow water equations.