Why does water only flow downhill? At first it seems that conservation of energy answers this question: water in a lake can't flow up the streambed because this would require gaining gravitational energy, and it has no other kind of energy to trade in for it. However, this just leads to a different question: when water flows downhill into a lake, what happens to the energy? It would seem that if the energy stays in the lake, the water could run back uphill at any time -- but this would give a lake that continues to swirl and thrash endlessly. And indeed it does, but as the water flows into the lake, its kinetic energy becomes divided up into ever more complex motions on a finer and finer scale, until every molecule is doing something different; then we can only describe this energy in terms of an increase in temperature of the water.

We still could ask why the process can't be reversed, so that the local motions would combine to give larger scale motion, until finally the thermal energy of the water in the lake would be converted into visible motion. This is not prohibited by the principle of the conservation of energy, and in fact the answer is that this could happen, but we will never observe it, for the same reason that we do not expect to pour a thousand pennies from a jar and have them all land heads-up: there are many different ways to distribute the energy, and having all the molecules going the same way at once is just one of these countless possibilities.

The Second Law of Thermodynamics

There are many ways to share something, and only one way not to share it. Nature doesn't care which of the possible outcomes we observe, and the result is that if sharing is possible, it will always happen.

This idea gets a fancy title: the Second Law of Thermodynamics (the First Law of Thermodynamics is just conservation of energy). It can be stated generally as the idea that a system never proceeds from disorder to order spontaneously (which implies that systems will always proceed towards disorder if they can). It is at its heart a probabilistic statement -- "never" really means "it is very unlikely" -- but physics has found ways to evaluate the probabilities involved, and the result is that long before you will observe an exception to the Second Law, you and every one you know will win the million dollar lottery -- several times each!

The Second Law of Thermodyanamics wouldn't mean anything if "disorder" could not be measured. But it can, and the name for what is being measured is entropy. The entropy can be calculated once we know how many ways there are to achieve a physically equivalent system, and it is zero if there is only one way to do it. So a perfectly ordered deck of cards or a set of pennies all heads up or a perfect crystal with all the atoms in place and not moving has zero entropy. High entropy is a "disordered" deck of cards (in no particular order), or a set of pennies with about equal numbers up and down, or a gas with the atoms placed at random and moving in all directions at once. And then one statement of the Second Law of Thermodynamics is that the entropy of the universe never decreases.

Some examples:

• At the end of a hand of cards, we shuffle them, by changing the positions of some of them. This generally makes the deck less ordered, though it is just as likely to produce a deck in perfect order as it is any other one of the zillions of possible ways to arrange it. The point is that a good hand is a rare thing, while at the end of the hand the cards have been sorted a bit by how they were played; almost any change of the deck is likely to prevent getting too many unusual deals.
• Energy flows from a warm object to a cooler one, because this shares the energy; there are more possible physical configurations with the energy shared that with it concentrated.
• Water evaporates into dry air, even though it costs energy to separate the water molecules from each other. Having all the water in the glass and none in the air is a more ordered situation than having some of the water evaporated: think of all the places the escaped molecules can be! This happens even though it requires the evaporating molecules to steal more than their share of the energy, which causes the remaining water to cool.
• Consider a mixture of ice and salt (or any other chemical that will dissolve in water). The salt cannot enter into the ice crystal structure (and in fact, when you freeze salty water the ice formed contains very little salt), so the only way to mix the salt and the water together is to form a liquid. It takes energy to turn solid ice into liquid, which comes from the kinetic energy of the molecules: the salt-ice mixture is colder than the original ice, by as much as 10^o C.
• A tiny seed in plain dirt gives rise to a flower; snow forms flakes of geometrical precision; people build cathedrals and write symphonies. Order happens! Is this a violation of the Second Law? No, because we are only looking at part of a system. Sunlight comes to earth, and a corresponding amount of energy is radiated away. We live in a river of energy moving from high concentration at the sun to extreme dilution in the dark of space, and stealing a little energy and order is no more amazing than getting energy from a running stream using a water mill.

Using heat and making things cool