Thanks for clarifying that.<quoted text>

In the classical case, a micro-state is defined as the specific position and momentum of every molecule in the system. Since both position and momentum are continuous variables, the number of micro-states would be infinite in every case. In classical statistical mechanics, this was worked around by using integration in phase space (6 dimensions-3 for position, 3 for momentum) and a bit of hand waving. It was also found that identical particles needed an additional division by the factorial of the number of particles. There was no explanation for this in classical studies.

When quantum mechanics was discovered, it was found that there are two fundamental classes of particles: fermions and bosons and that they obey different statistics. Essentially, fermions cannot be in the same state as each other: this forces them apart. The fact that electrons are fermions is behind the stability of all the matter around us. Bosons, on the other hand, are more likely to be in the same state as not. This means that a collection of bosons will have a lower pressure than a similar collection of fermions.

In the quantum description, a micro-state is simply a quantum wave function that describes the entire system. In counting such functions, we look at a basis of the relevant space of wave functions. This gives a finite number when the total energy and volume of the system are specified. It is one of the assumptions in statistical mechanics that all micro-states are equally probable at equilibrium. This may fail out of equilibrium, however.

The upshot is that the number of available micro-states is determined by the total energy, composition, and volume of the isolated system. So a debris field and a house have the same number of micro-states at equilibrium.

In terms of our current dispute, we can distill it down to your final two sentences. One question I have is whether the "total energy" you refer to includes the rest energy (intrinsic mass) of the particles, which would be non-zero even at zero-K, right?

UC may think he understands what a micro-state is but shows no evidence of understanding what a macro-state is or that any particular debris field = 1 unique macrostate (temp etc being constant), and that in this respect each debris field is as unique as each house.

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