mitochan said:Hi. You see the truth. You can see beautiful derivation in
http://www.feynmanlectures.caltech.edu/II_19.html
Laplace's equation is a partial differential equation that describes the behavior of a scalar field in a given space. It is used to solve problems related to electrostatics, fluid dynamics, and heat transfer.
The Principle of Least Action is a fundamental principle in physics that states that the path taken by a system between two points is the one that minimizes the action, which is the integral of the Lagrangian over time.
Laplace's equation and the Principle of Least Action are both used to describe physical systems, but they are different concepts. Laplace's equation is a mathematical tool used to solve problems, while the Principle of Least Action is a fundamental principle that describes the behavior of physical systems.
Laplace's equation is used in many fields of science, including electromagnetism, fluid dynamics, and heat transfer, to solve problems related to these systems. The Principle of Least Action is used in theoretical physics to describe the behavior of physical systems and predict their future states.
Laplace's equation can only be applied to systems that are linear and have a steady state. The Principle of Least Action is limited to systems that can be described by a Lagrangian, and it does not take into account quantum effects. Additionally, both concepts have limitations in their applicability to complex systems.