I haven't studied thermodynamics and entropy for years, but...

[Buckeye_Democrat]

I don't think '12345' would represent less entropy. Information-wise, I think entropy more accurately represents the number of ways a system can be arranged. Those five digits can be arranged in 120 ways, and that's a better indication of the entropy than the actual ordering.

Temperature is the average kinetic energy of the objects in the system.

Entropy has the dimension of energy divided by temperature. So if the total energy is constant in a closed system, the increase of entropy indicates that the average kinetic energy has decreased in some process and hence the decreased kinetic energy must be in other forms, which increases the ways the total energy has been arranged.

I suppose another way to look at it is that not all collisions are elastic, where both the momentum and kinetic energy of a system are conserved. In inelastic collisions, some of the energy is transformed to radiation.

Someone with a PhD in physics could probably explain it better, and more accurately, than me. Entropy has a reputation for being a tricky concept, so I'm not going to pretend that I totally grasp it.

There's an idea from Erik Verlinde called "Entropic Gravity" which, if true, would do away with the need for "dark matter" to explain the observed rotations of galaxies and galaxy clusters. It's far beyond my understanding!
https://en.wikipedia.org/wiki/Entropic_gravity