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As the science of thermodynamics developed beyond its industrial roots, two powerful ideas came to the fore - equilibrium and irreversibility. These ideas were already implicit in studies of heat. You have already seen that heat flow from a hot steak to a cold plate is an irreversible process. The effect of this process is to cool down the hot steak and warm up the cold plate, leading to a more uniform distribution of temperature. The heat transfer continues until a state of equilibrium is reached, characterized by a completely uniform temperature.

Understanding the conditions needed for equilibrium, and the irreversible processes that drive systems towards equilibrium, has deep consequences throughout the sciences. For example, under normal conditions, the equilibrium state of carbon is graphite, rather than diamond. Fortunately, the processes that restore equilibrium are very slow in this case, so diamonds do not perceptibly turn into graphite. But, under some rather extreme conditions, diamond is the equilibrium state rather than graphite, and this fact can be used to create new diamonds from soot. More generally, thermodynamics determines which states of matter are in equilibrium under any given set of conditions.

Entropy and the second law of thermodynamics provide the key to understanding equilibrium. An isolated system, free from all other influences, may undergo various spontaneous changes, some of which will increase its entropy. If the total entropy increases during a process, as it usually does, the process is irreversible - it is impossible to return to the starting point, leaving no other traces, since that would require a decrease in the total entropy, which is impossible. Once the entropy has increased, it cannot decrease again. An isolated system therefore approaches a state in which the entropy has the highest possible value. This is a state of equilibrium. In equilibrium, the entropy of the system cannot increase (because it is already at a maximum) and it cannot decrease (because that would violate the second law of thermodynamics). The only changes allowed are those in which the entropy remains constant.
Continue on to 3.2 Equilibrium and irreversibility, part 2 of 2