The classic example of entropy: cream is added to coffee, creating a new mixture that is equal parts coffee and cream as well as being a new temperature, dependent on the temperatures of the coffee and cream before mixing. Information about the coffee and the cream become inaccessible to us, there is just this new thing. Our species will add cream to coffee in an attempt to differentiate and assemble until there is more of the former than the latter in the mixture, which will homogenize nonetheless, the new mixture simply containing more traces of us than it otherwise would have. Traces that will be further diluted by time.
The coffee cup is small, the earth is slightly less small. Entropy can be talked about on any scale. What is circumscribed as a system is a case by case concern. Anything that can be circumscribed is like a machine, the parts and internal interactions of which can variably be known. There simply isn’t enough time or technique to measure every one of these machinations, meaning that some concepts are good only for precise, small, insignificant measurements or large, analogizing conceptualizations.
The sun and the earths molten core provide all of the energy with which substances on the earth do useful work. Life occupies the thin interface between these two heat sources that drive all movement. Yet, the sun also contributes to the erosion of rock, a deteriorative process the entropy of which is as much in the loss of energy in performing the operation as it is in the progressive mixing of formerly distinct substances, in the irreversibility of the process itself. There is no such thing as a truly reversible process - the existence of which would allow for work to occur without the production of entropy. Science, even given its occupation with what actually is, often enjoys deluding itself with theoretical impossibilities. Processes can at least exist on a continuum of more to less reversible. The more irreversible the more entropic, but also the more productive. Coal and oil are finite because as we burn them their energy is dispersed in a way that we can’t recapture, their energy being lost to our use. Too much energy is released from its subterranean subterfuge and into the atmosphere, living things die. Energy is about homeostasis, availability, displacement, not about its being finite or potentially destructive.