Having “cracked the textbook” once again, I’d like you to “get” why entropy is so important.
Consider two billiard balls. We use billiard balls since they give you the right mental model of what is happening. When they hit, very little energy is lost and the most is conserved as Kinetic Energy.
First, let’s consider the fundamental laws of classical physics. There are three conservation laws, laws that say something must always exist unchanged.
One is the conservation of mass. Over time, mass doesn’t disappear. It may change forms and move around, but it isn’t created or destroyed. (Relativity aside, of course, which merely shows that mass and energy are interchangeable.)
Two is the conservation of momentum. No matter what happens in a collision, the net momentum of all the particles is always going to stay the same. Momentum is mass times velocity, which includes direction and speed. A bullet coming out of a gun has a lot of momentum even though it is small. A truck barreling down the freeway also has a lot of momentum because it is massive, even though it is much slower than a bullet.
Einstein’s theory of relativity shows us that light particles are more than just waves, they actually have momentum and can slow or speed things up.
Three is conservation of energy. Energy is the sum total of work done. Work, in the physical sense, is force times distance. Energy is one of those concepts that takes a long time to “get”, but once you understand how energy works, it makes a lot of things much easier to think about.
OK, back to the billiard balls. When two billiard balls hit each other, those three measures are conserved. No matter what happens, the total mass, total momentum, and total energy is conserved.
What about when two billiard balls of the same mass approach each other at the same speed? At the end of the collision, both billiard balls bounce off each other. Each billiard ball leaves the way it came. This is important, for reasons you’ll see in a moment.
Now, let’s talk about temperature. For a long time, temperature was one of those things that puzzled physicists. That’s because the various models they came up with to describe temperature were unsuccessful in describing actual phenomena. Over time, physicists realized that there was some other quantity that was being conserved, although what it was, exactly, they couldn’t exactly say. However, they came up with an equation that looked something like this:
internal energy = temperature x (magical quantity) - pressure * volume
Chemists will quickly realize that an important term is missing. That’s the term that has to do with chemical or phase energy. Don’t worry, we can add it back in later. We’ll just ignore state or chemical changes for now, and pretend that we are working with an ideal gas.
With this equation, all the phenomena that real gasses exhibit are mostly predictable. Things make sense, and you can start finding new conservation laws.
What this describes is that as you put energy in or take energy out, something has to give. Either the pressure or volume changes, or the temperature changes. But the temperature doesn’t change in the same way all the time—it changes in proportion to this magical quantity. But what is interesting is that the magical quantity seems to suck energy and never give it back.
This magical quantity is named “entropy”, which comes from Greek. The “en” part means “internal”, and the “tropy” part means “turning”. This describes how some of the energy you put into your system is “turned” to “internal” energy that is lost forever.
It wasn’t until later that someone was able to build a statistical model of what is actually happening inside the ideal gas that entropy could be described mathematically. Naturally, curious physicists looked at the math and tried to make sense of it. This is where we get the idea of “disorder”. Entropy represents the statistical probability that the particles are doing one thing and not another.
After all, you could imagine that all the gas were on one side of the chamber, leaving a perfect vacuum on the other. All the quantities (mass, momentum, and energy) would be conserved, and so this is a certainly possible state. However, our statistical understanding say that this isn’t likely to happen at all, and so we won’t see that in practice.
That is, you won’t see it after some time has passed. You can certainly start things off with the gas all on one side, but over time, things will get more disordered.
And this is where the 2nd Law of Thermodynamics comes from. It is stated in two forms. One is “Entropy increases or stays the same over time.” No process will reduce total entropy, and at best, you can only keep it constant. The second form, which took some time to realize, is “Heat doesn’t flow from cold to hot (without additional work added.)”
To understand what the second statement means, we need to understand what heat really is. Heat is a kind of energy, but not energy in the normal sense. It’s a magical kind of energy that doesn’t exist at a molecular level. It obeys a whole different set of laws.
Heat is energy transferred (in what form, we can’t say) from something hot to something cold. That is, energy is lost from the hot thing and energy is added to the cold thing. Heat does not flow from a lower temperature to a higher temperature. Heat is not radiation, it is not collisions, it is not air currents or anything else like that.
Now, you can think of heat as being made up of all those microscopic interactions including radiation and convection and conduction and whatever else you can think of. That’s because, at the molecular level, when two systems meet, the particles of each do interact. But if you try to work the other way, from the molecular on up, you are going to miss an important aspect of temperature and heat.
What follows is the entire point of the post.
Let me describe this for you. There is a way to transfer energy into a system and cool it. Strategically radiating something, you can actually cause its temperature to decrease. You can even decrease the entropy of the system. Let me explain what I mean.
You may have heard of Maxwell’s Daemon. Imagine two chambers of gas connected by a tiny hole that only one molecule could pass through at a time. That hole has a door which can be open or closed at any time. A tiny daemon sits at that hole and opens the door or closes it in an instant according to how he likes to.
Let’s suppose that the daemon decides to open the door when a fast particle were approaching from the left, or when a slow particle approached from the right, and keep it shut otherwise.
If the door is open when a fast particle approaches from the left, then the right side increases its total energy by the energy of that particle, and the left side loses the same amount of energy.
If the door is open when a slow particle approaches from the right, then the left side increases its total energy by the energy of the particle, and the right side loses the same.
Over time, net energy would flow from the left to the right. All of the laws of conservation would be satisfied—except the 2nd Law of Thermodynamics. That’s because the right side would increase in temperature, while the left would cool. Heat would be flowing from cold to hot.
Such a situation could be possible if such a daemon could exist. But more importantly, on the microscopic level, we see that not all energy transferred will heat the system it is transferred to. Sometimes, the energy transferred cools the system it is transferred to. Yes, adding energy to a system can cool it!
Well, we can invent other scenarios that behave much like the above. What if the daemon had a set of mirrors. He used these mirrors to direct light from the sun to strike fast particles in such a way as to reduce their momentum. All the conservation laws would be satisfied—except the 2nd Law of Thermodynamics. But the earth would cool as more radiation flowed from the sun.
Of course, Maxwell’s Daemons don’t exist except in our imagination, as far as we know. We don’t even know how such a thing could be built. Such a thing would have God-like powers, the power to create and destroy entire universes.
But Maxwell’s Daemon does show something important. That is that not all photons from the sun increase the temperature of the earth. However, thanks to our understanding of probability and our understanding of that magical quantity entropy, we know that when the earth is cold and the sun is hot, the vast majority of photons do increase the temperature of the earth. But as the earth warms, more and more photons are actually cooling the earth. If the earth were to reach the same temperature as the sun, then the energy flowing from the sun would neither heat nor cool the earth.
This is why heat cannot flow from cold to hot. And this is also why looking at energy alone is a futile exercise. We must use the generalizations that Thermodynamics give us and abandon our microscopic model and understanding when we think about temperature and heat.