Question

What is the reason behind the fact that natural systems always tends to evolve towards configuration of minimum potential energy?

Answer 1

See below

Explanation:

This phenomenon is everywhere: an apple falling off the tree; an electron dropping into the lowest -13.6eV orbital in the Hydrogen atom; a pendulum or spring mass system always reverting back to the equilibrium position.

And the simplest (unhelpful) answer is that that is how nature behaves.

What is noticeable is that in all the examples given, one can look at forces rather then energy. So gravity pulls the apple of the tree and keeps the pendulum swinging, and the electrostatic Coulomb force can be seen to behind the electron-proton attraction and also the springiness of a spring at a molecular level.

Mathematically, the link between force and work/energy is revealed in calculus. So the work, `W`, done on/energy added to a system by force `bb F` is a line integral:

• `W = int_C bb F \ d bb r`

Which leads us to another, perhaps more familiar, relationship, Newton's 2nd law:

• `bb F = m bb a`

The problem is that `bbF = m bb a` cannot be derived. It is true because it always happens.

Except that,...., it can be derived as a special case from both the Schrodinger Equation and Special Relativity, but SE and SR are in turn built upon postulates. ie things you assume but can't prove/ derive.

So all we've done is pass the buck. But I think it's OK to do that :-) or so he seems to think.

Richard Feynman on the Why? question

The other thing that might be worth mentioning as a footnote is entropy , another bizarre phenomenon that seems to crop up everywhere. Even in the cleanest case, when the electron settles in the lowest energy orbital, a photon is fired out.