I hadn't heard of the fluctuation theorem, so thank you for pointing it out to me. However, I don't really see the relevance. Based on my (admittedly cursory) investigation, the fluctuation theorem is a generalization of the second law, which not only states that entropy will increase on the large scale but also predicts the statistics of small-scale entropy fluctuations. It can be applied to classical or quantum systems, but it doesn't have anything specifically to do with quantum mechanics. More importantly, it is not derived from fundamental principles, any more than the second law is.
What the FT does is link QM with classical thermodynamics. As the ensemble becomes smaller, the behavior becomes less and less classical, and more and more QM, and the possibility of entropy reversal consequently greater and greater. The FT allows calculation of how much entropy reversal is possible for how long for a given ensemble and how likely it is. In the classical limiting case, it says that entropy is irreversible and holds the 2LOT as applying strictly only in that limit; in the quantum limiting case it says that entropy and entropy reversal are equally likely. The actual test of the FT involved an experiment in which entropy was reversed for a large (in quantum terms-- but small in classical terms) ensemble, for a limited time.
It's important to differentiate the FT from a theory: it is a mathematical theorem and therefore subject to proof, which no scientific theory is or can be. As such, I believe your claim that it is not derived from fundamental principles is incorrect, because the derivation is also subject to proof, and as with all theorems it begins with axioms, which are about as fundamental as it gets. And given it's been experimentally verified, in addition to being mathematically proven, I think that there is sufficient evidence to accept it wholly, and to accept that its axioms are sound.
I'll freely admit that the irreversibility of most dynamics is a well-established empirical result, but squaring that result with the reversal symmetries of classical and quantum dynamics is one of the great unsolved problems in physics.
I think that is because there is commonly confusion between time reversal symmetry, which only requires ergodic consistency between the initial and final conditions of the system with the definitions of initial and final being dependent on the time direction chosen, and the true results of running a movie backwards, viz., the smashed egg jumping up from the floor to the counter and becoming whole. The second is not time reversal symmetry. It is time reversal of mechanics, an entirely different concept.
Note carefully that ergodic consistency and time reversal symmetry are two of the three fundamental assumptions (axioms, IOW) that the FT is based upon. It is
not based upon time reversal of mechanics, and does not require it.
Of course, one can't recover the original state in practice. But in principle, if you exactly reverse the appropriate quantities in your final state and then let it evolve, you'll see the dynamics run in reverse until the original state reappears. The only reason we can't usually do this is because "exactly reversing the appropriate quantities" is extremely unfeasible.
Let me try this again: if you start with the final state, not just in practice but in theory, and run it backwards, it is not guaranteed either in classical or quantum mechanics that you will get the original initial state that the final state came from, nor is it necessary that it be so for the mechanics to be time reversal symmetric. It is only required that the original initial state be
one possible outcome from that final state run backwards. Since random choice from a range of possibilities is part of both the classical and the quantum mechanics it is unreasonable to expect it to be otherwise.
IOW time reversal symmetry is not logically associated with the results of running a movie of the interaction backwards. Those results are only one possible outcome. Even supposing it were practical to begin from the final state and run the physics backward, there is no guarantee that the original initial state would be recovered; however, if a large enough ensemble of runs were considered, it is guaranteed that the original initial state would be one of the outcomes seen in that ensemble.
There are many possible histories that could lead to the die lying on the floor at that exact angle with the six side uppermost, and even many that would have it in the exact position and orientation it is in. And there is no way to distinguish among them given only the die resting on the floor in a particular position and orientation.
The "irreversibility of interaction" is not a physical principle I've heard of in any context. In classical mechanics, every interaction is fundamentally reversible, and irreversibility only arises in the appropriate statistical limit.
I'm aware of that, and it seems to me that this is due to the need for scientists to specialize. Nobody's looking at the "big picture." Also there is a lot of confusion because of the difference between the reversibility of mechanics, which is not manifest in reality, and time reversal symmetry, which is.
In the Copenhagen interpretation of quantum mechanics, each measurement collapse is fundamentally irreversible, regardless of statistics.
I don't like Copenhagen because it concentrates on "measurement." Measurement is only another interaction, and should be treated as such. That's one reason why I like Consistent Histories.
That's just the thing: un-measuring a state would violate quantum mechanics. If you collapse a state through measurement and then "run the movie" in the opposite direction, you'll see the un-observed components of the wavefunction spontaneously reappear, which is not something that quantum mechanics allows. The fluctuation theorem may give irreversibility, but quantum measurement collapse actually gives time asymmetry in the strictest sense.
Since I see time reversal symmetry as only requiring ergodic consistency, not certainty of obtaining the original state from the final state, I don't see a problem as long as at least one possible outcome of reversing time is the original state. Being able to run the movie in reverse and that being the only possible outcome is not, in my opinion, necessary. Running the movie in reverse and it always coming out like the original state is not necessary.
