There’s a concept that’s crucial to chemistry and physics. It helps explain why physical processes go one way and not the other: why ice melts, why cream spreads in coffee, why air leaks out of a punctured tire. It’s entropy, and it’s notoriously difficult to wrap our heads around. Entropy is often described as a measurement of disorder. That’s a convenient image, but it’s unfortunately misleading. For example, which is more disordered – a cup of crushed ice or a glass of room temperature water? Most people would say the ice, but that actually has lower entropy. So here’s another way of thinking about it through probability.
This may be trickier to understand, but take the time to internalize it and you’ll have a much better understanding of entropy. Consider two small solids which are comprised of six atomic bonds each. In this model, the energy in each solid is stored in the bonds. Those can be thought of as simple containers, which can hold indivisible units of energy known as quanta. The more energy a solid has, the hotter it is.
It turns out that there are numerous ways that the energy can be distributed in the two solids and still have the same total energy in each. Each of these options is called a microstate. For six quanta of energy in Solid A and two in Solid B, there are 9,702 microstates. Of course, there are other ways our eight quanta of energy can be arranged. For example, all of the energy could be in Solid A and none in B, or half in A and half in B. If we assume that each microstate is equally likely, we can see that some of the energy configurations have a higher probability of occurring than others. That’s due to their greater number of microstates. Entropy is a direct measure of each energy configuration’s probability.
What we see is that the energy configuration in which the energy is most spread out between the solids has the highest entropy. So in a general sense, entropy can be thought of as a measurement of this energy spread. Low entropy means the energy is concentrated. High entropy means it’s spread out. To see why entropy is useful for explaining spontaneous processes, like hot objects cooling down, we need to look at a dynamic system where the energy moves. In reality, energy doesn’t stay put.
It continuously moves between neighboring bonds. As the energy moves, the energy configuration can change. Because of the distribution of microstates, there’s a 21% chance that the system will later be in the configuration in which the energy is maximally spread out, there’s a 13% chance that it will return to its starting point, and an 8% chance that A will actually gain energy. Again, we see that because there are more ways to have dispersed energy and high entropy than concentrated energy, the energy tends to spread out. That’s why if you put a hot object next to a cold one, the cold one will warm up and the hot one will cool down. But even in that example, there is an 8% chance that the hot object would get hotter.
Why doesn’t this ever happen in real life? It’s all about the size of the system. Our hypothetical solids only had six bonds each. Let’s scale the solids up to 6,000 bonds and 8,000 units of energy, and again start the system with three-quarters of the energy in A and one-quarter in B. Now we find that chance of A spontaneously acquiring more energy is this tiny number.
Familiar, everyday objects have many, many times more particles than this. The chance of a hot object in the real world getting hotter is so absurdly small, it just never happens. Ice melts, cream mixes in, and tires deflate because these states have more dispersed energy than the originals. There’s no mysterious force nudging the system towards higher entropy. It’s just that higher entropy is always statistically more likely. That’s why entropy has been called time’s arrow. If energy has the opportunity to spread out, it will.