The 2nd Law of Thermodynamics is primarily a law of change. It applies to systems free of external influences. In a sense, everybody is familiar with the 2nd Law. It distinguishes the possible from the impossible in ordinary affairs and gives us our sense of the passage of time. Divers do not rise out of the water feet first and land on the diving board. Cups of a hot liquid left to themselves do not get hotter.

The Law may be stated in many different forms –

It was first applied to the transfer of energy in steam engines.

The 2nd Law (a)– In a heat engine the heat energy cannot all be transformed into mechanical energy (work) but is always accompanied by heat flow into a cooler part of the system

One form of energy cannot be transformed completely into another form without "loss." No engine can work at 100% efficiency. There is always a transfer to low grade heat due to friction or conduction. Low-grade heat is that where the temperature differential is too small to do work.

Since heat is simply the random motion of molecules, more heat means more randomness, or disorder. This bouncing around of molecules is more disordered than any other form of energy. Therefore, the ultimate conversion of any form of energy to low grade heat means an increase is disorder.

More generally, it was observed that:

The 2nd Law (b)– Heat never flows spontaneously from a cooler body to a hotter one. (A hot liquid left alone never gets hotter.)

It was concluded that the natural tendency among all molecular crowds is towards a spreading out of their energy, or an increase in randomness, which means an increase in disorder as time goes on.

Therefore it follows:

The 2nd Law (c)– The direction of spontaneous change for an isolated system is from order to disorder.

Since the arrangement of molecules with equal molecular speeds in randomly oriented directions is the most probable one, and since all other examples of change exhibit the same movement toward a state which is more probable, the 2nd Law can be phrased as a law of probability, hence

The 2nd Law (d)– The direction of spontaneous change for an isolated system is from an arrangement of lesser probability to an arrangement of greater probability.

Suppose we put some cool gas on one side of an empty divided container and some warm gas on the other side. This a special arrangement, a kind of order. If we remove the divider we always find some slow moving (cool) molecules have moved to the other side and some fast moving (hot) ones have done like-wise. The total energy in the container has remained the same but the arrangement is gone, the mixture inside the box has become unspecial. The entropy of the whole container has increased.

It is conceivable, but improbable, that at some time in the future all the slow moving molecules could accidentally again wind up on one side and the fast moving ones on the other. However, the more probable arrangement is a mixture. That is what we find in nature. Without additional input systems will move from special to the unspecial, from the less probable to the more probable, from order to disorder.

Summary (so far) - Entropy is the name given to:
— the amount of energy that cannot be converted into work
— the measure of the extent of disorder in a system
— the probability of the arrangement of the parts of a system
Systems of greater probability, which means greater disorder, are systems of higher entropy.

The following statement of the 2nd Law is the most general. On the basis of all experiments and observations —
The 2nd Law (e1)– The entropy of an isolated system remains the same or increases
The 2nd Law (e2)– The total entropy of a set of interconnected systems remains the same increases.
The 2nd Law (e3)– The entropy of the universe tends toward a maximum.

Note: The First Law of Thermodynamics states that the energy of the universe is constant.