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--- equations:hamiltons_equations [2018/05/06 13:52]
jakobadmin [Intuitive]
+++ equations:hamiltons_equations [2018/11/23 13:28]
129.13.36.189 [Why is it interesting?]
@@ Line 310: / Line 310: @@
 This comes at the cost of doubling the size of the system.
+----
+<blockquote>You get equations like Hamilton's whenever a system *extremizes something subject to constraints*.   A moving particle minimizes action; a box of gas maximizes entropy.   <cite>[[https://twitter.com/johncarlosbaez/status/1065715514381557761|John Baez]]</cite></blockquote>
 <tabbox Origin>
-"Hamilton’s equations and the [[equations:maxwell_relations|Maxwell relations]]—are mathematically just the same. They both say simply that partial derivatives commute." See  https://johncarlosbaez.wordpress.com/2012/01/19/classical-mechanics-versus-thermodynamics-part-1/
+"Hamilton’s equations and the [[formulas:maxwell_relations|Maxwell relations]]—are mathematically just the same. They both say simply that partial derivatives commute." See  https://johncarlosbaez.wordpress.com/2012/01/19/classical-mechanics-versus-thermodynamics-part-1/
 and  https://johncarlosbaez.wordpress.com/2012/01/23/classical-mechanics-versus-thermodynamics-part-2/