New Criticals

A Couple of Things About the Second Law of Thermodynamics


The second law defines a quantity known as entropy, which has units of energy per degree or energy divided by temperature, and it says that this quantity can only increase or stay the same over time. It is usually stated for an isolated system for the same reason that the first law is usually stated for an isolated system: Just as the energy of an open system can change by coming and going from the surroundings, the entropy of an open system can decrease as long as more entropy is given off to the surroundings and the net change in entropy over time is positive. That’s basically the trick to what are called “dissipative systems.” They are becoming more organized but “paying for” that organization by mixing up their surroundings more than they are organizing themselves. I like to avoid these details, however, by saying instead that the second law says that any irreversible process increases the entropy of the universe. The microscopic, idealized processes of individual molecules or individual waves in mechanics are reversible and do not produce entropy. Any real, macroscopic process, however, is irreversible and does produce entropy. So let me try and explain what it means to “produce entropy.” 

The thing to do now is leverage the fact that we understand, or maybe its better to say simply that we believe, that energy can be “neither created nor destroyed” and ask, given this fact, what do we mean when we say that we “use” energy? What is the actual meaning behind the phrases “We obtain energy from food” and the phrase “The energy for life comes from the sun?” Let’s start by looking at the earth as a “closed” thermodynamic system.

The term closed system means that energy enters and leaves the system boundaries (as light or heat) but mass does not. This is only an approximation because the earth is truly an open system, mass can enter and leave just like radiation, but its a good approximation because the amount of mass that enters in the form of meteorites and the amount of mass that leaves on rockets are very small compared to the overall mass of the earth so we can ignore mass transfer for purposes of explanation and focus on the incoming and outgoing radiation. So, the closed system has a few options with respect to overall energy flux. More energy can go in than comes out, in which case the temperature of the system will increase; more energy can go out than comes in, in which case the system will get colder; or the input and output can balance over time, in which get it, the average temperature should stay the same. The earth is getting hotter by the way, and that’s a problem. But for the moment lets just focus on some short time scale during which life (and countless other irreversible processes) are going on on the earth but during which the average temperature of the earth is staying the same--Energy is being “processed” constantly by the biosphere, yet the total energy that comes into the earth and the total energy that leaves roughly balance out and energy is never lost--what is happening? In simple, physical terms the biosphere is converting light to heat. In the language of statistical thermodynamics, irreversible processes are producing entropy. Let me try to explain how these phrases are equivalent descriptions.

A high energy photon, say with an ultraviolet wavelength that is energetic enough to cause a genetic mutation, can be thought of as a concentration of energy in space relative to lower frequency, thermal radiation. When it hits the earth’s atmosphere, it suddenly encounters a dense fluid (air is a fluid--you spend every moment of your life immersed in a fluid) compared to the relative emptiness of space and it collides with the molecules in the air. Of course, the photon is really a wave being scattered but to intuit the statistical counting process involved I think it’s easier to visualize a “packet of energy.” Each random interaction diminishes in some way the energy of the “packet,” but energy is not lost--it is merely spread out, becoming less concentrated. When radiation is diffuse enough that it can no longer excite electrons in the bonds of organic molecules we call it heat instead of light, but these words are defined relative to the bond energy of organic molecules. However, electromagnetic radiation is an expression of the same fundamental interaction whether or not it is concentrated enough to excite the pigments in your eyeball and thus be “seen.”

So the more the wave is scattered the less energetic “it” becomes, or using the particle metaphor, the more the photon bounces into molecules, the more it is broken up into smaller “pieces.” This “increase in the number of pieces” is my loose, everyday rendering of the increase in entropy due to increasing available quantum microstates. If “quantum microstates” sounds like mumbo-jumbo then I promise you that nothing essential is missing from your statistical understanding of what’s happening if you simply imagine a solid chunk of energy breaking into small bits of energy and thus increasing the number of ways to arrange the pieces. This may, however, be very misleading when trying to understand the wave nature of nature but that’s language for you, no single metaphor lets you tell it all.

Let’s think about how life is involved in this process. Our solar photon can do much more than simply be scattered by the atmosphere, it might also be absorbed by a chlorophyl inside a leaf. The thermodynamics of photosynthesis are too complicated to discuss in detail yet, but the overall process is basically going to synthesize sugar which will make more plant and/or eventually be eaten by an animal and turned into motion and/or more animal. The point to notice is that once it gets involved in the machinations of life, the energy that was in our photon has a much more tortuous and complicated path to follow before it escapes back out to the atmosphere almost entirely degraded from concentrated, high energy-radiation into diffuse, thermal radiation which is now energetic enough to wiggle and vibrate chemical bonds but not to excite the electrons in them.  As a result, there are “more quanta” of energy leaving the earth than entering, even though the the total energy entering and leaving is the same. This increase in the number of "pieces" of energy is a direct measure of the total entropy production of the earth and all life on the earth. According to Sean Carrol, this ratio is currently about 20 to 1, so you can picture uv light entering the earth as being made up of 20 dollar bills, and the thermal radiation leaving the earth as being composed of one dollar bills. Overall though, the value in equals the value out and the total cash amount never changes, it is only ever split up into smaller and smaller fractions. Out there in space, the dollars are still breaking into pennies. Bear in mind though, radiation is radiation whether it’s “light” or “heat” just like cash is cash whether its Franklins or Washingtons.

So here's an intuitive, alternative formulation of the second law: Energy becomes as spread out in space as it can as time passes. Frank Lambert is responsible for this formulation, and he has also devoted his life to removing the word “disorder” from textbook discussions of entropy. His website is great if you want to learn more. Anyway this spreading is a statistical consequence of what happens to randomly moving particles that are always bumping into, “interacting with” one another.

Map displaying energy density of radiation leaving earth

The mathematics of how irreversibility emerges statistically will require it’s own discussion, but for now let’s attempt to visualize some familiar physical processes that display irreversibility. The simplest possible case is dropping something, like a rock. When held in the air the rock has concentrated gravitational potential energy that turn into kinetic energy as it drops. Say you only drop it a few feet, not enough to break the rock. But do you hear it hit the ground? If you do then that means the collision caused a lot of local wiggling of the air molecules and it gave off a little bit of heat, and this energy has been dispersed in such a way that it can never be recovered. In an idealized limit, you can call such a process reversible if you imagine performing it infinitely slowly, such that at no point in its trajectory does the rock cause even the slightest disturbance of the air around it. The point to take from that example is that the reversible case is an idealization. Its also a good one in this case because the entropy produced by the collission is small enough to be negligible. But if the rock is dropped at any real speed, there will be some random mixing of the environment around it, and thus some irreversible component to the process. A clearer example is to imagine a liquid being poured onto a flat surface. It is dissipating gravitational potential energy as it falls, which causes it to stay together, but once it’s on the flat surface the gravitational potential is the same in every direction the liquid can move. What does it do? It spreads out, obviously.

Diffusion of a dye molecule throughout a liquid is another example of random thermal motion causing probabalistic mixing leading to a final state where the distrubution of matter or energy is equalized.

Finally, lets look at a chemical reaction that matters to you, such as combustion, which is the net result of how we use the oxygen we breathe to yank electrons away from the carbon atoms in the food we eat. Chemists talk about the “electronegativity” of the oxygen molecule, what this jargon means is that molecular oxygen, the O2 we breathe, represents a deeper potential well for an electron than does a carbon-hydrogen bond such as the ones in fat and sugar. This is why we can “oxidize” these fuels. Another way to think of it is that fat or sugar are fuel sources which represent concentrations of electrons with high electrostatic potential and being bound to an oxygen nucleus is a pit into which these electrons fall in order to dissipate that electrostatic potential. When this happens, heat is realeased (it’s combustion). This heat represents the further probabilistic mixing of the universe which is the true rationale for why combustion occurs in the first place. If it weren’t entropically favorable to release heat to the surroundings, combustion would not occur, and you would not breathe oxygen or be here in the first place.

As I hope it is beginning to be clear, entropy has nothing to do with the vague notion of disorder and has instead everything to do with why ordered structures and organizations exist at all--Life is an evolving network of interactions that involve ever more complex cycles of matter which result in more and more irreversible processes which produce more and more entropy. Entropy itself, however, is simply the word we've affixed to the probabilistic tendency of energy to equalize its distribution everywhere in space, or saying the same thing, to spread out as far as possible. As much as it sounds like a macabre joke, and it partially is, everything happens for a reason. That reason is the production of entropy. Beginning with the next post, we can begin to see how this reason organizes and explains the evolution of life.


Thumbnail Image: Closed systems subject to energy flux may be spontaneously driven to states of higher complexity and organization.