it is the change in entropy that ultimately provides us with the answer to why systems will naturally evolve in one direction with time and not the other: systems always evolve in time in such a way that the total entropy of system + environment increases. If you observe a system in which the entropy appears to decrease, you can be sure that somewhere there is a change in the entropy of the environment large enough to make the total entropy change positive. for example, suppose that in a closed system i drop an ice cube in a container full of hot water. heat will flow from the hot water to the ice. the temperature of the hot water drops and the ice melts simultaneously until both bodies of water reach the same temperature and form a homogeneous luke-warm body of water. the cooling process of the hot water is a negative entropy change. in other words, the entropy of the hot water decreases. (the hot water changes from a relatively disorganized state to a more organized state.) the melting process of the ice is a positive entropy change. in other words, the entropy of the ice increases. (the ice changes from a relatively organized state to a more disorganized state.) it turns out that the positive entropy change of the ice is greater than the negative entropy change of the hot water. in other words, if you observe the hot water in which the entropy appears to decrease, you can be sure that there is a change in the entropy of the ice large enough to make the total entropy change positive. if "sh" is the negative entropy change of the hot water (sh < 0) and "si" is the positive entropy change of the ice (si > 0), then sh + si > 0.