Laplace's equation vs Principle of Least Action?

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SUMMARY

The discussion centers on the relationship between Laplace's equation and the Principle of Least Action, highlighting their similarities in solutions. Specifically, it notes that the solution to a one-dimensional Laplace equation results in a straight line, paralleling the straight line that minimizes action in classical mechanics. The conversation references Richard Feynman's lectures, particularly his exploration of minimum entropy generation in quantum mechanics, raising questions about its applicability in quantum contexts.

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  • Understanding of Laplace's equation in mathematical physics
  • Familiarity with the Principle of Least Action in classical mechanics
  • Basic knowledge of quantum mechanics concepts
  • Ability to interpret mathematical derivations and physical principles
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  • Explore the derivation of solutions to Laplace's equation in various dimensions
  • Study the Principle of Least Action and its applications in classical and quantum mechanics
  • Investigate Feynman's lectures on minimum entropy generation and its implications
  • Research the relationship between classical mechanics and quantum mechanics in terms of action principles
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Students and professionals in physics, particularly those interested in mathematical physics, classical mechanics, and quantum mechanics. This discussion is valuable for anyone seeking to understand the foundational principles that connect these areas of study.

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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.
 
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mitochan said:
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?
 

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