The Second Law of Thermodynamics and Entropy

The First Law of Thermodynamics tells us that total energy is always conserved in any process — but it says absolutely nothing about the direction in which a process actually proceeds. Ice does melt spontaneously at room temperature; the reverse — water spontaneously freezing at room temperature — never happens, even though the First Law would not itself forbid it (energy would still be conserved either way). Some additional principle is clearly needed to explain, and to predict, which direction a process will actually take. That principle is the Second Law of Thermodynamics.

The Second Law is most usefully expressed, for chemistry, in terms of a state function called entropy, $S$, which is commonly understood as a measure of the randomness, disorder, or number of energetically equivalent microscopic arrangements available to a system. A gas has higher entropy than a liquid, which has higher entropy than a solid of the same substance, because a gas's molecules can be arranged in vastly more ways in space and can spread their energy over vastly more possible motions. The Second Law states:

That is, the total entropy of the universe (system plus surroundings together) must increase for any spontaneous process, and remains unchanged only for an idealized, perfectly reversible process at equilibrium. It is essential to note that this criterion applies to the system and surroundings combined, never the system's entropy in isolation — many perfectly spontaneous processes (such as water freezing below $0^\circ\text{C}$, or a gas condensing to a liquid) actually decrease the entropy of the system itself, while releasing enough heat to the surroundings to increase the surroundings' entropy by an even larger amount, so that the total still increases. …