Final answer:
If the entropy of the system decreases, the entropy of the surroundings must increase by a larger amount as stated by the second law of thermodynamics which ensures the total entropy of the universe does not decrease.
Step-by-step explanation:
If the entropy of the system decreases, then the entropy of the surroundings must increase by a larger amount. This is because of the second law of thermodynamics which states that the total entropy of a system and its surroundings cannot decrease over time. The second law implies there are only two possibilities for entropy changes: entropy remains constant for a reversible process, and it increases for an irreversible process.
When a system loses entropy, the lost entropy is transferred to the surroundings, and due to the spontaneous nature of most processes, the entropy of the surroundings increases by a larger quantity. This ensures that the total entropy of the universe either stays the same or increases. If a process results in a decrease in a system's entropy, such as becoming more ordered, the surroundings will absorb not just the quantity of entropy lost by the system, but additional entropy as well—often due to energy transfers at different temperatures—resulting in a net increase in the total entropy.
Example: When heat transfers from a hot object to a cold one, the entropy decrease in the hot object is less than the entropy increase in the cold object, due to a larger change in entropy at lower temperatures, resulting in an overall entropy increase.