The system in the paper is what I run my roasts with. Every bean that I roast goes through it, so I have data on a few different origins and varietals. There is some variation largely based around age of the coffee. The peaberry behaves a bit differently too, retaining a lot of water. First crack and the duration for the curves in the paper occur at 9:18 at BT 93°C, I will say though, it seems the pattern that humidity increases before first crack occurs. My hypothesis is that initially when steam is generated it can get out of the bean without breaking the structure. However, during first crack steam is generated faster than it can be released, which builds pressure, eventually fracturing the bean. Once the structure is broken, it can be released faster, which is why there is an increase in the drying rate and large humidity spike. This could also account for the expansion of the bean throughout process, but there are also other volatile organic compounds and carbon dioxide produced as well.
My apologies, I'm not 100% clear on what you mean by density of a vapour, but I'll attempt to share what I know anyway. I think water is a very interesting substance as it's so abundant and so necessary for life, at yet, it behaves strangely. It is the exception, not the rule in a lot of respects to what we know about chemistry of other liquids. Water has this property of being a light molecule but expands by a disproportionately large amount when compared to other compounds with the same molecular weight. This is due to the hydrogen bonds in water, which are quite strong molecular bonds. Water has a high boiling point comparative to its molecular mass. This results in a molecule that absorbs lot of energy, in its liquid state, to change temperature. It takes a lot more energy to transition it into a gas, and when it does transition it greatly increases in volume. It's also abundant and therefore cheap. All these properties are great if you're trying to run something like a steam turbine, but what has it got to do with coffee?
I think that most of the energy expended is consumed transitioning water from liquid to steam. In terms of the overall energy balance of the roaster once you transition through FC the amount of energy you need to keep increasing in temperature is diminished. Sometimes I see the endo versus exothermic argument made. I don't think that the roast is ever truly exothermic, as in it produces its own energy (from chemical reactions). I think it just appears so, as it's so easy to get into that runaway state where there is so much excess energy in the machine.
With respect to stalling, the steam leaving the bean can go from a high-pressure state to a low-pressure state when it exits the bean. It may be this expansion is something like adiabatic cooling, where that expansion of water vapour in the drum is the causing the temperature decrease. Caveat though that no process is ever adiabatic. There is always some heat transfer, but it might be at least a way to get an idea of the total energy available if all the water was to suddenly go from say high pressure inside a bean, to low pressure in the drum. Also it might be good to think that if a roaster was trying to pull back on a process to prevent that runaway state, then the roaster might already be in an energy deficit. The gas might be off, there's little or no heat being supplied to the system, so instead the hot metals or hot air in the drum is in fact what's pushing the roast along at that point. If there was a sudden decrease in energy available to the coffee, say by 'endothermic flashing' (Illy), or steam rapidly expanding, this could send that balance way into the negative, resulting in a crash. If this were the case you would see more crashing with roasts with high moisture content. In Australia, it seems the African varietals are the ones with both high moisture content and also the ones that have a propensity toward crashing. In my 1kg, I don't really see it much, but my batch sizes are very small, therefore the total water in the system is lower so you may not expect to see the effect. I also installed new elements which are rated up to 4.2kW, which is a lot more energy compared to the mass of the coffee then some other roaster designs.
So how this all effects how I roast coffee is that the machine largely does the roasting by itself. I set the end temperature, charge temperature and the machine lets me know when to open the top chute, and when the roast will likely be finished. It uses that sudden humidity spike to telegraph first crack and takes control of the fan and the element. It also tells me when to drop the coffee out of the drum. I'm looking replacing these manual operations with actuators soon, so that as long as the roaster is fed coffee it will keep churning it out. The weight is also predicated using the RH probe and compared with the actual result at the end. Most times it's pretty close (within 5 grams or so), however this can drift as the stack fouls up and the readings become less accurate. So rather than having profiles for just one coffee (i.e. Sumatran (6months old), hot day), the machine looks at that change in temperature, what its prediction model is saying and adjusts itself up and down. As long as the batch size in the ball park, it will quite happily chug along by itself. Long term the idea would be to implement most of this in software so that it can be added to other roasters. I think automated roasting is very possible and is coming along much sooner than a lot of people think. This technology has been around for a long time in the hydrocarbons industry, so I think we're due. Using the mathematical model from the paper, we picked up a couple of silvers at the Australian International Coffee Awards, so I think it seems to be working. But I will end this (sorry for the essay) by saying this is just how I think it works. This is a deceptively complicated thermodynamic problem, that is complex. I'd like to think that there are definite answers, but modelling wet steam systems is really hard. I think that all models are wrong, including this one, but some are useful. So I hope this was useful in explaining your question. Also thanks for reading if you've gotten this far. I live for this stuff, which is weird and I don't even fully understand it, but I really do love it.