If the oil dispersed itself similarly to the acetic acid discussed previously, there would be many more water molecules involved in clathrate structures. So this solution sacrifices the entropy increase associated with even dispersal of a solute, for the benefit of a reduced amount of order introduced by a clathrate structure. A more biochemical example is the folding and unfolding of proteins. A polypeptide that has folded into a functional protein is much more restricted in orientation than an unfolded polypeptide, which is like a string that can be bent and twisted into countless conformations. So for a protein that undergoes folding, the entropy change is negative, whereas for a protein that unfolds, the entropy increases, and the change is positive.
Chemists use entropy as a tool for understanding spontaneous change.
For a reaction, entropy can be used to predict whether it will proceed spontaneously. Organisms are open to the universe because they respire, excrete waste, generate heat, etc. So the only way to use entropy as a determinant for change in an open system is if you consider the entropic effects on the entire universe, which is very difficult to measure. It is this D G that provides a very useful gauge as to whether a reaction will proceed in either the forward or backward direction in a given environment and with a specific concentration of reactants. To give you an idea of why the free energy is a better way to determine whether a reaction is spontaneous or not, note that while protein folding leads to a decrease in entropy, it is still a spontaneous process inside of cells.