It is hard for me to understand the wikipedia entries regarding entropy and thermodynamics but it seems that the fundamental cause has something to do with probability.
Is this correct?
Yes.
Here's a simple example (this is called the "Ehrenfest urn model"). Consider two containers and N coins, labelled 1 through N. N is a large number. Every instant you randomly pick a number between 1 and N, and move the corresponding coin from whichever container it's currently in to the other. The quantity of interest is the number of coins in each container, or more conveniently, the fraction
f of the coins that are in container A at any given time (i.e.
f={number of coins in A}/N).
What will happen to
f as a function of time? It's probably clear that
f has an equilibrium value, namely 1/2 (if that's not clear, I can explain). It may also be clear that any state where
f differs significantly from 1/2 will not last long (i.e. not much longer than N instants), and that once
f gets near 1/2. it will experience only small fluctuations around it. All of those statements are true if N is large (bear in mind that this is a simple model for a physical system where N is often of order 10
23 or larger).
What does this have to do with entropy? Entropy is simply (the log of) the number of states that share some macroscopic property, like a value of
f. For example, suppose N is even. Then there are N choose N/2 (that's a very large number) states with
f=1/2. But there are only N states with f=1/N, and only 1 with f=0. That means that with
very high probability, low entropy states (like f=1/N) will evolve into high entropy states (like f=1/2 or near it) rather than lower entropy states (f=0), simply because there are many more high entropy states (by definition).
What makes this a useful concept is that when N is very large, the number of states near f=1/2 is vastly, mind-bogglingly larger than the number of states near f=0. Therefore the chance of the entropy decreasing is absurdly small, so small it may never have happened in the history of the universe. As a result, the 2nd law of thermodynamics is called a "law", even though it is in fact "merely" probabilistic.
This is the reason drops of ink dissolve in water and never re-form, it's why you never see people leaping up out of swimming pools and landing on the diving board above an undisturbed water surface, it's the essence of life, and it explains why time has a direction. It's one of the simplest, most beautiful, and most profound ideas in physics.
