Are Boltzmann brains really possible? My question is the following: can particles luckily aggregate
and instantaneously generate a full adult body? In general,
can a full body appear from "nowhere" (meaning not following
the canonical biological development from a single cell), for instance right in front
of me?
When people talk about Boltzmann brains
they usually assume that this is the case, but what is the
physical ground for such a scenario? Is it a real possibility
(independently of how unlikely that would be) compatible with
the laws of physics (if so, which), or is it possible in a merely loose sense
of the word?
Thank you for your attention.
 A: The number for the probability is hugely small. Not at all like the previous answers. The only way the argument make any possible sense if you you consider an infinite universe, with an infinite number of particles, or an essentially infinity of multiverses. You multiply infinite by the small probability and yes you can get Boltzmann brains. You can also get probably about the same number of demons who go about destroying them. Everything can happen in eternity. 
Consider the possibilities. Treat the case of the brain having $10^{26}$ particles that are the ones that define the possibles states, as in @Koo's answer. We'll see that his calculations are way off. In reality it's a lot more, but let's still stick with that number. 
If you had 2 particles with 6 possible microstates each you'd get $6^2$ possibilities. The possible positions of one particle is not 3, but 3 dimensions multiplied by the number of possible positions in one dimension, say 1 position every 1 angstrom in the brain. That roughly gives you $10^9$ positions. Momentum in each dimension say is another $10^9$. Total possible states is $(10^9)^6$ = $10^{54}$ possible single particle states. With the number of atoms or molecules stated, the number of possible combinations is (number of states) raised to the number of particles, or roughly $(10^{54})^{10^{26}}$. 
That is roughly a probability of ONE in $(10^{10})^{26}$ particles that will maybe form a Boltzmann brain. That is ONE in $10^{260}$. In actual fact the number is probably less because multiple particles could do what we said one particle does, so there is some interchange of particles where the end result is essentially the same Boltzmann brain. So figure that out, with permutations, let's say reduce the number by $10^{26}$. That still ONE in $10^{234}$.  
The only way it works is if the universe of particle, or the multiverse, is so huge as to be infinite. It does not work for our observable universe of about $10^{80}$ particles. You'd need about $10^{154}$ of our visible universes to get one Boltzmann brain. 
Maybe I'm off some, but if you do it exactly assuming random works, our visible universe is not enough to come out with one. 
A: Boltzmann brains do not require entire bodies to be formed, because all our experiences and memories can be translated to some state of the brain (similar idea to brain in a vat).
I'm not considering subatomic particles, nor different electron energy levels, and limiting myself to human brains instead of any possible consciousness, but the core argument of probability should still hold.
There are $10^{26}$ atoms in the human brain, but $10^{79}$ atoms in the observable universe.
There is a very low probability of $10^{26}$ atoms taking on a specific structure as the brain. From statistical mechanics, given a macrostate of $10^{26}$ atoms with total energy $E$, these atoms can be in any combination of microstates such that the total energy is still $E$.
Each microstate of a single atom is a 3-dimensional position vector. Assume the atom can take 1 of $10^9$ discrete positions per dimension within the cubic brain of side length $0.1m$. To require that these atoms have the one specific arrangement of a human brain would require specifying the values of all $((10^9)^3)^{10^{26}}$ microstates. The probability of which is just $1/(all\space possible\space states)$.
[possibility of Boltzmann brains existing in our observable universe redacted after discussion with Bob]
A: Yes, it is possible. You can take a brain and burn it to ash in a cramatory oven, or even gassify it if the temperature is above the carbon evaporation temperature. Now, run the movie in reverse, you have a way to make a brain from gas. It only requires the correct initial velocities 
and positions of all particles and radiation.
A: Boltzmann brains typically arise in any theory that attempts to explain the low entropy initial conditions of our universe in terms of a more generic initial state that would have existed earlier. The problem is then caused by the fact that around the time of the Big Bang, the entropy achieved a local minimum after which the entropy increased. Then, as observed by Boltzmann himself, you can  increase the probability of ending up with an observer, by decreasing the size of the part of the universe that has this local minimum in the entropy. The maximum probability is obtained for the smallest size possible where you could just render the observer you're aiming for.
This is then a paradox, because a Boltzmann brain would most likely be aware of random information which is not similar to what we are aware of. This seems to rule out any theory where in the past the entropy of the universe could have been large. It also poses a problem for theories where the universe will continue to exist indefinitely, because then we could arise in the far future after the heath death of the universe as Boltzmann brains, the question is then why we find ourselves living now and not later as Boltzmann brains. 
