Recently I have learnt Second Law of Thermodynamics that entropy for an isolated system is nondecreasing (such statement is true with a very high probability - I have heard that it can also decrease but chance of that is extremely small).
One of the most common exercises is to calculate entropy increase for an isolated system - room and ice cube, from some state A to state B where both bodies are in thermal equilibrium. What one can find is that even though total entropy of an isolated system increases (which is consistent with Second Law of Thermodynamics), entropy of one of the bodies decreases.
I understand that there is no fallacy here because obviously each of the bodies cannot be considered isolated systems for this process, but my question is this:
Why does Second Law of Thermodynamics holds only for isolated systems?
How can I intuitively understand this? Is it just that it is always consistent with experimental results therefore assumed to be true? Is there some fundamental principle underlying this problem?