“In those days I was essentially the only theoretical physicist there, whence things were not so easy for me, because I started mentioning entropy, but this was not quite fashionable, since it was regarded as a mathematical spook” – Max Planck, on his early days in Berlin, 1889.
Whether the bowling ball hits your face or the chair behind you is statistically and thermodynamically trivial, but it will become significant when you throw the ball through the wall and an ambulance takes you to the hospital where surgeons work all night putting your face back together. Similarly, whether the egg breaks into a bowl or onto the floor is trivial, but it will lead to a completely different evolution of the environment. These different physical relationships are obvious when they happen to you, but similarly random differentiations are happening around you all the time, so that the entropy of the universe is evolving in a way that can’t be represented statistically or thermodynamically. Once a system is in motion, the relationships between its moving parts are as significant, entropically, as the movements themselves. Every relationship between every moving part has entropic significance.
Entropy is the shape of moving objects in relation to themselves and everything around them, and that shape is what is meant by the measure of disorder. But disorder misses the point and is thoroughly distracting from the infinitesimal relationships that build into gross observations. Entropy would be the measure of information, order and energy in relation to one another if it were in any way measurable. What we have are hints, rumours and allegations. Entropy drives hardened physicists to whine like schoolboys.
Einstein was right. God doesn’t play dice. It’s much worse than that. God is a surfer.
Entropy is not just order versus disorder, it is the shape of the movable things and the groups of things that are moving together. A broken egg is the classical example of the irreversible increase in disorder, described as entropy, but statistical mechanics and thermodynamics have no particular preference for the original shape of the egg versus its cracked bits. That shape matters to us, because it was really handy to have the egg contained in its shell, and like the bowling ball that hit you in the face, the broken eggshell is a shape that is profoundly inconvenient. Unless you are making an omelet. Then you need to break some eggs.
Planck, Boltzmann and Clausius described the relationship between entropy and resonance, which is the absolute limit of what can be described mathematically. Entropy is a ghost, but it has a relationship between things that resonate are measurable, specifically, the momentum and temperature of matter. Entropy has a definite relationship with both of those functions, but it isn’t made of them. The actual entropy of a system isn’t the average momentum of the particles or the sum of the infinitesimal freedom of the particles that determine the wavelength of its blackbody radiation. The entropy of the system is the shape of every movement of every body and every differentiable part of those bodies at all scales, including the microscopic and the macroscopic bodies and the infinitesimal smoothness of their boundaries. The real entropy of the system is neither microscopic Boltzmann entropy nor macroscopic thermodynamic entropy nor blackbody radiation. The actual entropy has functions at every scale, from subatomic to muscular to waves, whorls and big solid objects.