Laplace's equation vs Principle of Least Action?

[Newton-reborn]

There seems to be a similarity between the solutions of laplace's equation and the principle of least action. e.g. the solution of a one dimensional laplace equation is a straight and the curve that minimizes the action is also a straight line. Was one derived from the other? Newbie here. Id appreciate any answer.

 

[mitochan]

Hi. You see the truth. You can see beautiful derivation in
http://www.feynmanlectures.caltech.edu/II_19.html

 

[andresB]

Hi. You see the truth. You can see beautiful derivation in
http://www.feynmanlectures.caltech.edu/II_19.html

uhm, in the note after the lecture, talking about currents and velocity distributions Feynman says "The question is: Does the same principle of minimum entropy generation also hold when the situation is described quantum-mechanically? I haven’t found out yet. "

Does this have a known answer?