My understanding of entropy: it is a measure of how big a system (matter + energy from a space region) is, and how much its components have interacted with each

My understanding of entropy: it is a measure of how big a system (matter + energy from a space region) is, and how much its components have interacted with each other: Entropy ~ log(number of possible system states). As the universe unfolds, systems originally isolated are starting to interact and to form bigger systems, hence the number of possible states increases, and entropy increases too.