Quantum Diaries

There are some things in science that are just so complicated that they cannot be explained to the uninitiated—things like quantum mechanics, the second law of thermodynamics, how a geek thinks, etc. To understand these things, it takes years of sleeping though dull lectures and late nights carous….  Oops, let’s start that again. It takes years of sitting in rapt attention at scintillating lectures, late nights studying (I have it right this time) and the secret initiation ritess. Don’t forget the secret initiation rites. But in this post, I am going to attempt the impossible and explain the second law of thermodynamics in a way that can be understood by the uninitiated. Fools rush in where angels fear to tread and all that. Now the second law is so complicated that there are several alternate but equivalent formulations. One is due to Rudolf Clausius (1822 – 1888). Now, this is very complicated, so take a very deep breath:

The second law of thermodynamics (Clausius): If you want your fridge to work you must plug it in.

See I told you it was complicated. There is an equally complicated version due to Lord Kelvin (1824 – 1907):

The second law of thermodynamics (Kelvin): The exhaust from your car motor will be hot.

Now you may think I am being facetious but I am not (OK, maybe about the scintillating lectures).  What a fridge does is cool things down by taking heat from the inside and depositing it outside, ie it takes heat from where it is cooler (the inside) and deposits it where it is hotter (the outside). An exact statement of the second law is that no process can simply do that: transfer heat from where it is colder to where it is hotter and have no other effect. In the case of the refrigerator, the other effect is turning electricity into heat. No fridge can be 100% efficient. Hence, you must plug your fridge in. Similarly, the Lord Kelvin statement is that no heat engine (e.g. your car motor, assuming it is not electric) can be 100% efficient and simply turn heat (the burning fuel) into mechanical energy (moving the car). Part of the heat energy must be wasted. In this case, the waste heat is in the hot exhaust.

The second law of thermodynamics, as these two examples illustrate, has significant implications for engineering and was derived in that context. It limits what even the best engineers can do and rules out a large class of second-law violating perpetual motion machines (Not to be confused with perpetual motion machines of the first kind which violate energy conservation, the first law of thermodynamics).

You may notice, that so far, this discussion has nothing to do with order, disorder or spontaneous creation or destruction that are so frequently associated with the second law (and used to create confusion and disorder). But there is yet another statement of the second law that does involve order and the concept of entropy. Entropy is simply a way of counting the number of microscopic states that correspond to given macroscopic state. Think of the air in a room: macroscopically it can be described by the temperature, pressure, and volume. Microscopically, it can be described by the location and motion of all the gazillions of particles that make up the air. Many different locations and motions of the air molecules correspond to the same set of temperature, pressure, and volume. Entropy is related to the number of different locations and motions (technically, the natural logarithm of the number) that correspond to the same temperature, pressure and volume.

One can crudely think of entropy as being the information content of a system—the information needed to specify the location and motions of the gazillions of air molecules in the example above. The lower the entropy, the less information content. Also note that ordered systems have less information content than disordered ones. Consider the strings:  1111111111111111 and 1907214836589457. The first is highly ordered and has low information content: it is just all ones. The second needs much more information to describe; each digit must be specified individually.  It is less ordered and hence higher information content and entropy.

A third equivalent statement of the second law is that the entropy of a closed system (ie one that does not interact with the outside world) can never decrease. Now the earth’s atmosphere and biosphere are not closed systems. They get energy from the sun and radiate it back out into space as thermal energy. The atmosphere and the biosphere together act like a giant heat engine using the sun as a source of energy and outer space as a sink for the exhaust heat (like the hot gas from the car engine). This heat engine lifts water from the oceans and puts it on mountaintops.  It drives all weather systems including hurricanes and blizzards, evolution, and life itself. It is this heat engine and the lack of thermal equilibrium that generates local regions of low entropy like the sheet of ice on the pond I skated on as child or the alligator in the southern bijou. The alligator, like all living things, has a high degree of order, hence low entropy and information content. Waste heat produced by living things is a side effect of maintaining that order. It might seem strange that I say living things have low information content but it would take much more information to describe in detail the location and motion of the atoms in an homogenized (think blender) alligator[1] than in a living one. There are simply many more ways to arrange the atoms in the homogenized version.

The second law of thermodynamics, being obscure when expressed in terms of entropy, is used to justify all kinds of nonsense. For example, evolution is sometimes claimed to be inconsistent with the second law of thermodynamics. But the second law of thermodynamics is not that obscure: it simply says you must plug your fridge in order for it to work. What’s obscure about that? Now, what evolution has to do with plugging in refrigerators is beyond me. After all, the earth’s biosphere is plugged directly into solar energy, bypassing the need for the electrical grid and cutting out the middleman.  I guess I will have to sleep through some more dull lectures to sort this all out.  Zzzzz.

Additional posts in this series will appear most Friday afternoons at 3:30 pm Vancouver time. To receive a reminder follow me on Twitter: @musquod