entropy may go "down" as well as up. A more sophisticated analysis is given by the entropy Fluctuation Theorem, which can be established as a consequence of the time-dependent MaxEnt picture. 3. As just indicated, the MaxEnt inference runs equally well in reverse. So given a particular final state, we can ask, what can we "retrodict" to improve our knowledge about earlier states? However the Second Law argument above also runs in reverse: given macroscopic information at time t2, we should expect it too to become less useful. The two procedures are time-symmetric. But now the information will become less and less useful at earlier and earlier times. (Compare with Loschmidt's paradox.) The MaxEnt inference would predict that the most probable origin of a currently low-entropy state would be as a spontaneous fluctuation from an earlier high entropy state. But this conflicts with what we know to have happened, namely that entropy has been increasing steadily, even back in the past. The MaxEnt proponents' response to this would be that such a systematic failing in the prediction of a MaxEnt inference is a "good" thing. It means that there is thus clear evidence that some important physical information has been missed in the specification the problem. If it is correct that the dynamics "are" time-symmetric, it appears that we need to put in by hand a prior probability that initial configurations with a low thermodynamic entropy are more likely than initial configurations with a high thermodynamic entropy. This cannot be explained by the immediate dynamics. Quite possibly, it arises as a reflection of the evident time-asymmetric evolution of the universe on a cosmological scale (see arrow of time). Criticisms The Maximum Entropy thermodynamics has some important opposition, in part because of the relative paucity of published results from the MaxEnt school, especially with regard to new testable predictions far-from-equilibrium. The theory has also been criticized in the grounds of internal consistency. For instance, Radu Balescu provides a strong criticism of the MaxEnt School and of Jaynes' work. Balescu states that Jaynes' and coworkers theory is based on a non-transitive evolution law that produces ambiguous results. Although some difficulties of the theory can be cured, the theory "lacks a solid foundation" and "has not led to any new concrete result". Though the maximum entropy approach is based directly on informational entropy, it is applicable to physics only when there is a