There are many answers on the site discussing motion of electrons in an electric potential field, See Why is voltage described as potential energy per charge?
but also mass tends to move toward a lower gravitational potential. I assume then that things in general tend to move toward a lower potential when the potential is defined so that it represents potential energy. However sometimes "potential" is used for a field that another field can be derived from usually by taking a gradient.
See What is a basic physics general definition of a 'potential'? for a discussion of the term "potential" in physics.
My question is:
Why physically do things in general tend to move toward a lower potential value in a potential field?
Do they in general? Is there a physical law? Is there a basic physical explanation? I know there are mathematical explanations. Does the potential have to be defined as potential energy for this to hold true? Also does this have to hold true if one field can be derived from another potential field. Etc. ..