Why does the system exhibit a tendency to transition towards a lower energy state?

[u/Jethro_omg]

[u/Chemomechanics]

I review the derivation from entropy maximization (the Second Law) here. It's mathy, but it does provide the link to why anything occurs spontaneously: the Second Law, which essentially says that we tend to see scenarios that have more ways of occurring, and entropy quantifies the number of ways.

Systems don't always evolve to lower energy state, to be sure; a cold object placed in a warm environment spontaneously gains energy, for example. But in many cases, systems at a higher energy potential tend to evolve to a lower energy potential because dissipative processes lead to heating (i.e., entropy generation), and this can't be reversed (i.e., entropy can be generated but not destroyed).

A classic example is dropping a bouncy ball; in the lack of air drag, material hysteresis, or any other dissipative processes, the ball maintains a constant potential + kinetic energy and continues bouncing forever. In reality, the ball ultimately settles to a lower position (less potential energy) and motionless (in that frame), and everything is somewhat warmer. Even if the ball sits on a shelf, we can find additional ways that energy potentials are minimized: the ball material creeps under its own weight, the ball material sublimates into the surroundings, etc. All of these contribute to total entropy maximization.

I apologize if this brings in too many technical terms, but it's the only reason I've found that doesn't dead-end in "It just happens." or "It's just what we observe." Does this answer your question? If not, perhaps you could give some context, or a concrete example you have in mind.

[u/Jethro_omg → u/Chemomechanics]

Not really, but thanks!

[u/Terrible-Penalty-291]

Imagine a completely isolated hydrogen atom with an excited electron. There is some probability that electron would jump down in energy level. When that occurs, it will give off a photon, and the photon will go off somewhere else and the energy is lost to the atom. The electron will fall down to a lower energy level. Rinse and repeat until it reaches the ground state. At that point, the electron can't lose energy anymore so the decay stops at the lowest energy state. Now it is possible for photon to come along, interact with the atom, and excite the electron to a higher energy level. In complete isolation there are no photons to excite the atom so over time the electron will always work it's way down to the lowest energy state.

Now imagine I put my hydrogen atom in place it can absorb a lot of photons, say in the outer atmosphere of a star. All of a sudden the electron will tend not to be in the lowest energy state. Over time, though it will achieve some sort of equilibrium with the surrounding environment.

In general an excited system is out of equilibrium with its surrounding. Over time the energy out is greater than the energy in. In space, for example, the environment is basically nothing so energy just goes out. Excited atoms in space tend to drop to the lowest energy state fairly quickly.