Theoretical proof forbidding Loschmidt reversal? In a famous debate, Loschmidt criticized Boltzmann's new theory of statistical mechanics by asking what would happen if the velocities of all the atoms were reversed. Typical objections are that such a reversal would not be possible without a fine detailed control over all the atoms of the system. However, spin echo experiments are a clear counterexample, albeit one restricted to very special cases. Is there any theoretical proof that without a fine detailed control over most of the atoms of a totally isolated system, a Loschmidt reversal would be extremely improbable? Remember such a proof would have to cover all sorts of elaborate complicated contraptions. Are reversals impractical for theoretical reasons, or because of a lack of ingenuity?
 A: It's impossible to forbid Loschmidt reversal by any theorem. Poincare recurrence is the dreaded counterexample. Finite closed systems will return arbitrarily close to their original state. The only thing Loschmidt failed to anticipate is it would take far longer than expected: an exponential time.
Using the second law to "forbid" reversals is circular because this very same result is used to "prove" the second law in the first place.
A: Lorschmidt reversal was an attack on naive Boltzmann ideas, based on a truncation of the full evolution to the Boltzmann equation. The Boltzmann equation is irreversible, it doesn't work backwards, and Lorschmidt is simply pointing out that it can't be right, because if you do a reversal, the Boltzmann equation must reverse in time, and it doesn't work backwards.
The reversal itself is not a problem for modern ideas--- you could probably actually do it. In modern ideas, the Boltzmann truncation is unnecessary, the entropy is directly defined on the unknown position of the state in phase space. So the entropy gain is only a measure of the loss of information. If you have a machine which can reverse the atoms' motion to approximately restore the original state, this means, by definition, that the information in the original state has not been lost yet, so the entropy has not gone up until the reversal no longer works.
There is no reason you can't build an (approximate) reverser, but it won't work perfectly. To make a perfect reverser would require infinite precision classically, it would require perfect knowledge of the particles (hence the reason you have a small entropy--- you know where everything is). Quantum mechanically, you would need to reverse outgoing photons, and do hopeless things.
The proof that you can't do Loschmidt reversal for a generic system is simply that it would reduces the entropy. Approximate reversals are fine, and the spin echo is an example.
A: Rather more hand waving than a "proof", but...
Note that in quantum mechanics the meaning of time reversal symmetry is subtly different then it is classically{*} and they system can not be expected to retrace it's history in reverse.
Add to this any degree of sensitive dependence on initial conditions (which is certainly possible in classical systems), and you can magnify quantum effects to macroscopic differences even in systems that appear to be fully amenable to classical description.

{*} The cross-section for the time-reversed reaction is the same as for the forward reaction in all cases{+}, but you can't pass "backward" through the "collapse" of the wave function (however you understand the selection of eigenstates to proceed).
{+} Well, for the CPT-reversed reaction, anyway.
A: The Loschmidt paradox is valid only in bounded systems with finitely many degrees of freedom, as the proof of Poincare recurrence fails in an unbounded domain, or if the number of degrees of freedom is infinite. 
As the true degrees of freedom are those of fields (though actually quantum fields), hence infinitely many, there is no Loschmidt paradox.
Actual reversal can be done experimentally ony for systems with a tiny number of degrees of freedom, typically just one.
