Every measure of entropy is pure fiction. From the statistical mechanics of the average momentum of the molecules of an ideal gas in isolation to the notions of energy and temperature, everything that describes entropy has to be made up. Having said that, observations have shown conclusively that the fiction is almost exactly what you would see if you could see what was going on in the non-resonant relationships between energy and matter. The inner transformation of matter really works like the distribution of momentum and position of molecules of an ideal gas in an isolated container. You just can’t observe it actually happening. Ever. That use of fiction to describe truth in a way that is unobservable is precisely why fiction is so important in all forms of communication, and why art can’t be removed from science without losing contact with half of reality.
Boltzmann’s equation made it possible to imagine the limit of entropy for a system with a certain amount of energy. No system will ever reach this limit, but it is tremendously helpful to know that entropic evolution has a limit, a maximum distribution of mass or momenta, and that the limit of entropic evolution can be derived statistically or probabilistically for well-defined, physical phenomena. The fictional description of real entropy provides a background of predictability to the random evolution of a real system. The fiction of entropy, like all great fiction, provides a teleological overlay for our chaotic moment-to-moment observations of reality. Boltzmann’s equation describes the relationship between the unobservable quality of entropy and the observable qualities of heat and moving parts, but it does not define entropy any more than the second law of thermodynamics defines entropy. It establishes that there is a relationship between the unobservable properties of matter and the observable properties, that this relationship is not trivial, and that the unobservable entropy of a system evolves predictably towards the maximum distribution of probabilities. This is wonderful, beautiful, magical work, but it is fiction. To say that experimental observations have shown that the statistical mechanical model of entropy is really what happens is like saying that Sense and Sensibility is a true story because it is based on countless hours of observations that show that this is really how people behave. We know that the unobservable relationships that make up the true entropy of the system are real, but we must appreciate that they will never be observable. Innumerable attempts to expand the scope of entropy mathematically have only served to make entropy more obscure because the actual relationships do cannot be represented mathematically.
The notion that entropy will result in heat death springs from the notion that entropy is making everything even out, or converge on a statistical average. While some things converge entropically, other things diverge entropically, and microscopically, there is a physical limit to the convergence. “Heat death,” as an idea, predates the discovery of quantum fluctuations in “empty” space, as well as quantum entanglement. But for most scientists, entropy still means the heat death of the afflicted system, even equilibrium, isolation and maximum entropy are physically impossible.