>Simple example: why ice melts in a warm room.
Ice melting is simply the water molecules gaining enough kinetic energy (from collisions with the surrounding air molecules) that they break the bonds that held them in the ice crystal lattice. But at the microscopic level it's still just water molecules acting according to Newton's laws of motion (forgetting about quantum effects of course).
Now, back on the topic of the article: consider a system of 2 particles separated by some distance. Do they experience gravity? Of course they do. They start falling towards the midpoint between them. But where is entropy in this picture? How do you even define entropy for a system of 2 particles?
> But where is entropy in this picture? How do you even define entropy for a system of 2 particles?
The answer is that this doesn't happen in a system with only 2 particles. The idea of gravity as an entropic phenomenon is that you introduce some other kind of particle that permeates spacetime, so there is no system that only contains 2 particles. You may use some idea like virtual particles from quantum field theory, or you may define "quanta of space time" as something that is not technically a particle but basically works like one in a handwavy sense.
But the basic point of these entropy based theories is to explain gravity, and typcilaly spacetime itself, as an emergent result of a collection of numerous objects of some kind. This necessarily means that they don't make sense if applied to idealized systems with very few objects - which is why they typically posit such isolated systems simply can't actually exist in reality.
Let me try to answer. Let's say the particles are experiencing gravity as a natural entropy phenomena. They will attract until they become so close that they are now seen as a single particle. The new system has a lower entropy and a higher gravity than before.
Explanation seems very rudimentary but that is the gist of the theory.
From my point of view, I might add the layer of information density. Every quantum fluctuation is an event and the more particles the more information is produced in a defined space volume. But there is no theory of information that is linked to the physics so ...that let me leave as that :).
Can you define quantum fluctuation?