Early on, in studying Big History, the relationship between complexity and energy becomes apparent. The more complex the system the more energy it needs. I’ll delve into this to a much greater extent later, but the most complex system we know of is our brain and pound for pound our brain uses more energy than anything else in the known universe. This includes stars and galaxies.
That said, with the rapid development of artificial intelligence the most complex system may be the systems developed for AI. Thus, energy needs may drastically increase.
On the other side, in decaying systems, complex systems will run out of energy as explained in the second law of thermodynamics, aka entropy. For the last 50 years, the thought was everything in the universe will reach a thermodynamic equilibrium aka heat death. When that happens, all complexity vanishes and what is left is nothing. This is entropy or the second law of thermodynamics. Lots and lots of information, both good and bad can be found on the internet on this law, duckduckgo it.
But there is a newer thought based on studying black holes with quantum mechanics and computer science mathematics. This is way beyond my ken, but it is important because it states that black holes will not die when it reaches thermodynamic equilibrium, but at that point the black hole continues to grow as expressed with quantum complexity algorithms. Those are similar to the second law of thermodynamics, but take us into the quantum realm of the universe. At some point, further in time, the black hole will cease its growth as forecasted by the quantum complexity algos. At this point, the whole cycle might start over again. Bang?
Here’s more by people who understand what they are talking about: