A cup of hot coffee is placed on a table.
The coffee cools down, the table and the air get a little warmer, until all have the same temperature.
The hot coffee gives energy to the environment.
Why does this not happen backwards?
(i.e. why doesn't the table cool down further and the coffee starts boiling, the energy concentrating in the coffee again?)

We have to understand why it is unlikely that the coffee gets all the energy if table and air are there.

Imagine the energy as a lot of balls, and the particles as some pupils.
We won't distribute energy among particles but balls among pupils.

2 identical balls are to distribute among 2 pupils (not necessarily equally). Which possibilities are there, and how many?

--|oo ; 3 possibilities.

Now let's double the number of pupils.
So now we can distribute 2 balls among 4 pupils. How many possibilities are there now?

--|--|--|oo  ; 10 possibilities. Only in three cases, that is in less than one third of all possibilities all balls go to the first two pupils.
By doubling the number of pupils we got three times the number of possible states.

With 20 balls and 20 pupils there are 69 000 000 000 possibilities.
Again let's double the number of pupils.
So now we can distribute 20 balls among 40 pupils. There are
2 800 000 000 000 000
possibilities! Only in 1/40000 of these  all balls go to the first 20 pupils..
Doubling the number of pupils meant 40000 times the number of possible "states".

What strikes here?

The number of possibilities rises steeper and steeper. It is more and more unlikely that the first half gets all the balls.

Now back to the cup of coffee. What happens if you allow for the energy to be exchanged among the particles of coffee and the particles of the environment?

(We don't know about possible "portions" of energy here. This is another chapter... let's stay simple, ok? ;-)):

The number of particles among which the energy can be distributed rises at contact with the environment
neither from 2 to the double (4)
nor from 20 to the double (40),
but (roughly) from
1 000 000 000 000 000 000 000 000 (particles of coffee alone)
to the double (particles of coffee+table+air+...).
That means: The number of accessible states rises inconceivably more drastically than in our example with the balls.

The states where the energy is concentrated among the particles of the coffee are just a very very minute part of all accessible states.
They are very very improbable , and this accounts for the empirical fact that they don't come back by themselves.

[auf deutsch]