Studies on the Studies on the
Entropy...last word EVOLUTION*
Aha! I knew that presumptuous message title would catch someone! I have become increasingly annoyed at suggestions here and elsewhere that Evolution violates the second law of thermodynamics. So, I hereby offer this monograph on the subject of the second law and entropy. And I then offer a challenge to anyone who is willing to use the substance of this piece to demonstrate how Evolution could possibly violate the second law. My qualifications? I have a degree in aeronautical and astronautical engineering and am a registered professional engineer.
There are several ways to express the second law of thermodynamics:
Kelvin-Planck: No cyclic process is possible whose result is the flow of heat from a single heat reservoir and the performance of an equivalent amount of work on a work reservoir. Energy interchanges can take place in any direction between any pair of work reservoirs, but energy exchange between a work reservoir and a single heat reservoir, with no outstanding changes in other systems, can proceed in one direction only -- that in which the work reservoir does work and the heat reservoir absorbs heat.
Clausius: No cyclic process is possible whose result is the flow of heat from a heat reservoir at one temperature and the flow of an equal quantity of heat into a second reservoir at a higher temperature.
It is, however, possible to carry out a non-cyclic process in which there is a flow of heat out of a heat reservoir at a lower temperature and a flow of an equal quantity of heat into a reservoir at a higher temperature.
Entropy Temperature is a measure of heat added or rejected for any substance undergoing a process at constant pressure or constant volume as long as the values of the factors of proportionality for the substance are known. These values are called the "specific heat at constant pressure" and the "specific heat at constant volume." It would be convenient to have a factor of proportionality with which temperature could be used to measure the heated added or rejected for any process, not just processes at constant pressure and volume.
As luck would have it, such a property exists. It is called _entropy_. Mathematically, T ds = dq, where T is the temperature of a substance, ds, is the incremental change in entropy and, dq, is the incremental corresponding incremental change in heat.
Back To The Second Law Besides the Kelvin-Planck and Clausius statements, the second law may also be expressed in terms of entropy. Entropy: In a real _closed_ system, total entropy can never decrease. It is important to note the restriction that the system must be closed -- that is, neither energy nor mass may cross the boundaries of the system. In other words, all elements initially in the system must be present and accounted for in the final reckoning. The entropy in parts of a closed system may decrease, but that decrease will be more than offset by an increase in other parts of the closed system. Let's look at a couple of semi-real examples. (Truly isolated systems do not exist.) I have a swimming pool divided into two halves by a thin dividing wall. Into one half I pour ink and into the other I pour water. I remove the divider and wait. The ink gradually mixes with the water (ignoring natural convection) and eventually I have a fairly uniform mixture. The entropy of the pool contents has spontaneously increased through the process of molecular motion.
I can reverse the process only by introducing into it Ken's magical ink-water separator. Using energy I have brought into the formerly closed system, I put the dividing wall back into place and grab all the ink molecules and put them in one side while at the same time moving all the water molecules to the other side. This could take a while.
I have restored the swimming pool to its original condition, but only by breaking into the closed system using energy I took from another closed system (one which I constructed around the pool before my original experiment began). Ken's magical ink-water separator runs off batteries which are now depleted so the entropy of the second closed system has increased as well. I could recharge the batteries, but I would have to go outside the second closed system and get an extension cord -- well, you get the idea.
Here's a different example: I have a closed system, a box of air through which neither energy nor mass may be transferred. In the center of the box I have one ice cube. The air is at 70 F and the ice cube is at 20 F. I return to the box some time later and notice a puddle of water where the ice cube used to be. The ice cube has spontaneously gone from a state of lower energy to a state of higher energy while the entropy of the ice cube itself has increased (water molecules move about at random, but are prevented from migrating in their solid state). The entropy of the surrounding air which has decreased in temperature has decreased (the pressure in the box has decreased due to decreased molecular motion of the air). The entropy of the entire contents of the box has remained unchanged.
Now that we have a better, non-ICR, understanding of what entropy is all about we can talk further about the misuse of the concept in areas other than thermodynamics. The concept of entropy, that is, the concept that things spontaneously move toward randomness and disorder has been captured and used as a metaphor in areas other than thermodynamics. These metaphorical applications of entropy are useful up to a point. They have been applied to social dynamics and information theory, but herein lies the rub. Metaphor has it's limitations. We learn about new things through metaphor. But unthinking extrapolation of a metaphor often fails. If I ask you what a UFO looks like, having never seen one myself, you might say, "It's just like an upside-down dinner plate that zooms through the air -- sort of a "flying saucer." You have just used metaphor to explain to me something to me that I have no acquaintance with. So far, so good. Carrying the metaphor too far, I imagine in my mind that a UFO is also made of plastic and has little daisies around the edges just like the dinner plates I have at home. See the problem? Metaphor has its limits.
The generalization that "everything tends toward disorder" when carried away from the subject of thermodynamics can easily lead to false impressions and error. Notice that in the Kelvin-Planck and Clausius expressions of the second law, I used some terms that have very specific meanings which may be easily misunderstood by those not familiar with the esoteric language of thermodynamics. One must have a thorough understanding of the definitions of heat reservoir and work reservoir. As in mathematics, precision of definition is demanded to avoid obfuscation.
The Challenge I hereby challenge anyone to use the strict definitions of the second law of thermodynamics to demonstrate that the fact of evolution in any way violates the second law. This is called science. Put up or shut up.
*from talk.origins 30 May 1994