6.2 Entropy and Probability

With just three dice in a box you will readily appreciate that at any time a less probable pattern may occur. Its not difficult to get {222} (W = 1 micro state). Its 1 out of 216 possibilities so we may say if we continue to shake the box randomly we will expect to see {222} every 216 shakes on average. Thats the price in entropy required to pay for the improbable {222}. Indeed if we were to count the number of shakes to successive occurances of {222} and divide the total number of shakes by the number of occurances we would observe the result approach 216, its asymptote to any degree of accuracy we like. So with just 3 particles we can see that the Boltzman Gibbs equation means an increase in improbability is a decrease in entropy that must be accounted for by the second law. Also the second law only applies to a large number of particle events not just particles, which is the basis of the probability which drives it.

The second law has to be formerly constrained to an isolated system of particles and a sufficiently large number of particle events to follow a predicted average behaviour. Under such circumstances the law states that the entropy (disorder) of the system must increase or at best remain constant (equilibrium). This predictability is about as near to an 'absolute' as you can get in science and yet it is driven by nothing more than the normal probability distribution with its central most probable outcome and an infinite number of less probable outcomes reaching all the way to the impossible.

So what is an 'isolated system'? It sounds simple enough.. a system which is so well insulated and sealed the inside is not effected by the outside. The only problem with this idea is, it's purely hypothetical.. we may be able to approximate it but in truth the only one we know of is the entire universe! The ultimate meaning of the second law is that the entropy of the universe must increase with time.

Have a particularly nice day..