Heat transfer by conduction works is also an illustration of this statement of the 2nd Law. When a hot and a cold body are initially in contact, the system is somewhat ordered, in that we know most of the molecules in the hot side are moving faster than those in the cool side. However, this degree of order is lost after the system has attained a uniform temperature.
The concept of entropy is introduced to characterize the order of a system. Qualitatively speaking,
Here, state is a very general term, and could include position, speed, etc. What the 2nd law states is then that
This is equivalent to saying that the number of states available to a system increases in general, by which the system thus becomes more disordered. In the coin example, the initial state (all heads up) was unique, whereas the likely finally state (roughly half heads, half tails) could be achieved in a very large number of different ways. The entropy increased.
A key point in this form of the 2nd law is that one is considering isolated systems. One could look at water freezing in a freezer and say the water molecules are becoming more ordered as the ice forms. This though would not violate the 2nd law, as the ice cube by itself is not an isolated system - one must include the freezer and the environment the freezer is in as also part of the system. One finds the entropy of the total system to be increasing over time, although the entropy of an individual subsystem may be decreasing. This is also relevant in the discussion of human evolution; by itself, the progression from simple organisms to complex human beings seems to violate the 2nd law of thermodynamics. However, one must in this remember that the human evolution chain is not an isolated system, and that one must include at least the earth and its environment in the total system. The entropy of this total system is then seen to increase over time, allowing for the fact that the human component of this system may be becoming more ordered.
The property of entropy in a sense defines for us a direction of time. If one took a film of someone dropping a jar of pennies which subsequently scatter all over the floor, then viewed later such a film would not appear unusual. However, if one ran the film backwards, so that we see a group of scattered pennies on the floor spontaneously come together inside of a jar all facing with their heads up, then we would know that something is wrong, even though such an event may be possible by energy conservation, for example. The fact that systems tend to become disordered in time gives us then a sense of direction of time. Note that this does not strictly contradict what we said in the first Chapter about time reversal symmetry of nature. The microscopic laws of physics say that any allowed process is also allowed in the time reversed direction. The 2nd Law of Thermodynamics is simply a consequence of the fact that some outcomes are far more likely to occur than others.