I like the way you describe the universe evolution as the quest for the most efficient way to reach equilibrium.

But the way you describe it leads inevitably to a halting problem.

In your description, the universe moves forward collecting information, until it reaches a specific state of equilibrium, where it has to wipe out all the stored information in order to restart again.

But there's another way to describe the universe that doesn't lead to the halting problem.

In my opinion, there's no need to choose betwen storing or discarding information at different phases of evolution, because both known and unknown informations shape each corner of the universe at all times.

There's no need for different types of cycles or special states, and all places and instants are equivalent.

The key to understand how this is possible lies in the time delays imposed by the finite speed of light and information propagation:

Every point in space has a unique point of view on how the rest of the universe is configured, but, at the same time, each point lacks the current information about the actual state of the universe at that moment.

Information has to propagate at the speed of light from place to place, so all local information is outdated by definition, and there's no way to ever get the required information about anything else existing in the universe to balance it perfectly in just one take.

As long as there's some distance (ie: Plank distance), there's a time delay (ie: Plank time), and a mismatch between the known status and the real status at that distance.

So the information present at each point is always outdated, and the actual information needed is always out of reach.

Then, every entity is trying to reach equilibrium as quickly as possible, but lacks the current information that defines the equilibrium condition it should be trying to reach instead.

The universe is always trying to solve a problem that is never the problem at hand.

If all entities could have perfect information about everything else at once, the universe would evolve from the initial state to the final state in one go (instantly), but that's not what happens.

Luckily for us, no entity is aware of the actual conditions that take place in the universe at the moment they observe it. There's always a "time distortion" in the data they collect, so they can never deal with the current situation perfectly.

John Archibald Wheeler said "time is what keeps everything from happening at once". And he was right.

The time delays caused by distance and propagation prevent each point in the universe from having the crucial information that would allow them to reach equilibrium instantly.

Each entity is trying to find the best way to deplete itself on its environment, but always using imperfect information.

That's why nature follows the least action principle: Everything happens as quickly as possible. Any difference tries to balance through all means available, but has to do so with the outdated information available.

So nature is not lazy. Nature is as efficient as she can be, given she is forced to use the local and outdated information available at each point each time.

Perfect information would drive the universe into equilibrium instantly, but the presence of outdated information forces the universe to chase an equilibrium condition that changes with time.

That's how the universe can have its cake and eat it: It is like a cat chasing his tail.

Reality is an emergent, overcomplicated Rube Goldberg machine trying to suppress itself, but failing spectacularly each time.