A Word On: Entropy

"Chaos always wins, because its better organized." 

Murphy's Law

This sentence has struck me ever since the first time I read it over 10 years ago. It holds a truly deep meaning about life in many levels and has been a source of wonder in my mind for the last decade or so, therefore it has gotten me asking, why does it hold so much truth in it?

Usually we tend to relate chaos with lack of order, with unbalance, with out-of-control situations around us, and overall an inevitable force around everything. It's only logical, if your bed is messy it won't tidy up itself unless you take time to clean it up (which is trully unfortunate because I really hate making up my bed). Or if you throw a bunch of pencils to the floor they won't go back up to your desk unless you pick them, nor will a broken phone unbreak, and the list could go on forever. These kind of situations have left to both a conclusion and a question: chaos is unvoidable, but why?

Image: pro.psychcentral.com/

One of the things I learned during my thermodynamic classes at college was that energy is basically everything. We use it in all of its forms (chemical, thermal, electrical, etc.) and it literally moves our world, ourselves and our universe. Energy is a property of the physical systems around us, and to my thinking it is best described as the capability of transformation. 

Bearing this in mind I came back to my messy bedsheets example; if my room was messy and the only way I can do something about it is spending some time and effort tiding it up, meaning I would have to spend some energy organizing my little chaotic system. So if I have to use energy to put chaos into order, hence transformating the system, maybe chaos is the opposite: detransformating, or, destroying order. 

At first it made perfect sense, energy is used to transform and create, chaos must then be the opposite, and be used to "destroy" the order in an non-reversible fashion. Non-reversible, keep this word in the back of your head. 

Image by: rawglor.deviantart.com

This hypothesis soon crumbled on the very principle that made me think of it: energy. 

If energy was a source of creation and chaos a source of destruction, how come you need energy to carry on a demolition of an old building? Why can you burn down a tree with thermal energy? 

The very idea of chaos being destruction of energy is wiped out by none other than the First Law of Thermodynamics: 

The total energy of an isolated system in a given frame of reference remains constant.

In other words, the total energy of a system cannot be created nor destroyed, because within its reference frame, it is conserved (for instance in time for continous systems). That's two birds with one stone, because this also implies that energy isn't created nor destroyed, it just transforms. This explains how I can knock down a building with some TNT: I'm using chemical energy (the exothermic, very unstable reaction going on with the TNT) to create kinetic energy (pieces of the building getting sent at high speeds in every direction). In conclusion, my first thought was wrong, as my idea of chaos being destruction of energy was nothing but energy just transforming and going elsewhere in the system. Back to square one, my room is still messy it seems.

So I was left wondering about energy going elsewhere, in some cases to places I don't want it to be (i.e. a pipeline loosing heat to the environment in an industrial process). What if chaos is related to this "mislead" energy?

Thermodynamics, luckily, had the answer just around the corner, and it came quick and forcefully: entropy. 

Image by: kidel.deviantart.com

The Second Law of Thermodynamics states:

The total entropy of an isolated system can only increase over time.

Putting it on perspective, the total entropy of the universe can only increase, meaning:

dS >0

This implies not only that you cannot have a system without entropy, but also that entropy's tendency in nature is to increase. This on itself will answer my initial question, but firs we need to know what is entropy exatcly.

Entropy is a concept that is hard to grasp outside a mathematical point of view. Elliott and Lira describe it as "A measure of disorder of a system", while Clasius (the man who coined the term in the first place) defines it as "a measure of the capacity for a body's energy to be transformed into useful work" (taken from Introductory Chemical Engineering Thermodynamics by J.R. Elliott & C.T. Lira).

Both are two sides of the same coin. Entropy is in fact a way to measure disorder in a system, by letting us know how much energy can be transformed in a way we want it or that we can take advantage of; therefore, entropy accounts for the energy that can be effectively used within a non-reversible system (remember this?)

In general, a non-reversible system is a system affected by entropy, meaning that the changes made in it cannot be turned all the way back. Let me illustrate this with a classical engineering example:

First, picture a turbine powered by steam at very high temperatures. The idea here is to take the thermal energy (heat) of our steam stream in order to make the rotor of the turbine spin and thus creat useful energy known as work. The following image can help you picture the situation:

Image: www.learnthermo.com

As you can see, steam enters the turbine (our system) at high pressure and temperature, and leaves with lower temperature and pressure, meaning some of its thermal energy was used to produce the work output of the turbine. Should this system have abscense of entropy, a.k.a. reversible, you should be able to obtain all the energy from the steam  and convert it into work. Yet if you observe in real life, the output conditions are not 100 % the results you should get if all the nrgy was to be used. The turbine has an efficiency, meaning it can only reach a certain maximum of usable energy, the rest goes elsewhere, the rest is entropy. This can be appreciated subtly by observing that the output steam is at a higher temperature than epected in a reversible system, and more subtly, in outer heating of the turbine and the sound that it produces. Energy is disoredered, it is transformed into "non-useful" things.

This hit me even harder than Murphy's law. It means that nature's natural course is towards entropy, towards energy just transforming into anything it can due to the lack of conditions for it to be useful to our eyes. Chaos always wins because entropy in the universe always grows.

If universe natural tendency is to nature, therefore it is to chaos, meaning that the reason of chaos being unavoidable can be explained by the unavoidable tendency of nature to entropy. Energy just goes wherever it wants and we can only use so much of it at optimal conditions. My room is full of entropy and it will remain that way (and increase) unless I lead my energy to clean it up. Perhaps Murphy didn't think of it from this point of view, but he was right nonetheless. However I don't think it's as fatal as he usually describes. Yes, entropy is unavoidable, but it can be minimized. Chaos is not the opposite of order, or energy, it's just a form of it, a very messy one, and as such it can be "tamed" into whatever we want.

In conclusion, chaos wins but only because it's energy that we are yet to tap. The universe tendency is to chaos, but only because we can only use so much of its energy effecively. Embrace chaos not as fatality, but as a measure of how much energy you can effectively use.