First of all, the Second Law of Thermodynamics dictates that in an isolated system the level of entropy will naturally increase over time. This is often expressed as energy within the system converting from more "useful" forms into more "useless" forms - such as heat. Many people interpret this as the level of "disorder" in the system increasing, but physicists refer to this as an increase in the number of available states of the system.

For example, let us imagine our system is a box of dice connected to a machine. Periodically, the dice are jostled by the machine. Over time, we would expect the numbers on the dice to mix into more and more complex combinations - this is because, statistically, the most probable numbers on dice rolls are those which contain the most number of combinations to get that result (think of rolling a 7 using two-dice - you can get it six ways: 1,6; 2,5; 3,4; 4,3; 5,2; 6,1) whereas the most improbable results can be found in only extremely specific combinations (the only way to get a 2 using two-dice is 1,1). It is these numerical combinations that physicists speak of when discussing the number of available states of a system (i.e. entropy).

Now, this brings me to my second point - by far the most spooky one. The Second Law, and the implication of Time's Arrow, are not actually laws in the sense that they are fundamental. They are actually statistical in nature, in that they can yield outcomes which we would find absolutely bizarre.

Let me return to our hypothetical box of dice with the jostling machine. As the dice are jostled and thrown around more and more, it is highly probable that they'll all come up as random numbers; likewise, it is highly improbable (the more dice the more improbable) that the result will come up all 6's. However, there is nothing fundamental in the laws of physics which would prevent that occurrence, it is just very unlikely to occur.

For instance, throw two dice and the chance of getting a 12 is 1/36, because you can only get a 12 by rolling a 6 on each die. That is...

P(12) = 1/6 * 1/6 = 1/36

Now, add another die. The odds of getting all 6's, giving you 18, is...

P(18) = 1/6 * 1/6 * 1/6 = 1/63 = 1/216

Add still another die, for a total of four. The odds of all sixes now is...

P(24) = 1/64 = 1/1296

and so on. Now, instead of just a handful of dice, let's imagine roughly one mole's worth of dice (where according to Avogadro's Number is 6.022x1023 particles/mole). This is because when we're dealing with physical systems, such as the molecules in a gas, we are usually dealing with large numbers of molecules - on the order of many mole's worth. So, with a mole's worth of dice, the chances of the dice all coming up 6's is...

P(all 6's) = 1/66.022x1023

which is a probability that is so small that for all practical purposes we call it zero. But note that while this probability is practically zero, it isn't technically zero - there is a chance, however small, that every single one of those mole's worth of dice could end up with a 6.

What's the point? This is the point... when discussing the Second Law, which states that the entropy of a closed system naturally increases (increasing "disorder" and increasing number of available states), this is really only an expression of the most probable result of a statistically random process. It is entirely possible, however improbable, that a closed system left to itself will randomly "order" itself. It is entirely possible that every single molecule in the atmosphere of the room you're in gathers up in the corner all at once, leaving you to suffocate - but since the probability of this freak event occurring is so small, we don't think about it.

In reference to Time's Arrow, we can think of the increase in entropy of a closed system as showing the direction of the flow of time. But remember, this is a statistical occurrence - time, by this definition, doesn't necessarily have to flow that way. Should the improbable happen, we would likely sense this as a reversal of the flow of time.

Hope this helps. Enjoy the freakout

The statistical nature of the Second Law doesn't have to do with the localized decrease in entropy (say, in the development of lifeforms from the biosphere, etc).

Remember, the Second Law states that isolated systems will increase their entropy over time. This means there is no energy input to the system from outside. And this is the fundamental flaw in every creationist argument related to the Second Law of TD. What amazes me is that it is such an amazingly simple concept, yet in order to make their worldview work they must suspend this basic law of physics. Magical thinking, indeed.

Specifically, in the case of the Earth, our planet is not an isolated system - it receives huge amounts of energy all the time from the Sun (just imagine what Earth would be like without the Sun). This influx of energy from outside our biosphere allows processes to take place all the time which result in an overall decrease in entropy on the planet (i.e. the development of life).

On a smaller scale, the entropy of your body decreases as you grow because you have an input of energy from outside your body - in the form of food. If you isolated yourself such that no energy could be input from outside your body - that is, you starve yourself - then the end result would be a localized increase in entropy. In other words, death.

This, of course, assumes the most probable result, something which I am quite confident will occur. So I suggest that you not stop eating anytime soon in the hopes of observing the freak statistical occurrence

I was reading a physicist whose argument was that the math of entropy/chaos could only result in order.