Entropy decrease results in memory loss

September 2, 2009

I found a fun arrow-of-time paper in PRL, arguing that dynamical decreases in the entropy of an isolated system are not at all impossible, just impossible to remember!

L. Maccone. Quantum Solution to the Arrow-of-Time Dilemma, Phys. Rev. Lett. 103:080401 (2009), arXiv:0802.0438

Abstract: The arrow-of-time dilemma states that the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e., entropy increases). I show that, within a quantum mechanical framework, all phenomena which leave a trail of information behind (and hence can be studied by physics) are those where entropy necessarily increases or remains constant. All phenomena where the entropy decreases must not leave any information of their having happened. This situation is completely indistinguishable from their not having happened at all. In the light of this observation, the second law of thermodynamics is reduced to a mere tautology: physics cannot study those processes where entropy has decreased, even if they were commonplace.

While interesting, I wonder if this approach is really promising. Basically, the author proves his Eq. (2), stating that the sum of entropy changes in a system A containing the observer and another system C equals the entropy change in a reservoir plus the change in the total amount of correlations (i.e., mutual information) between A and C. In the most interesting case when the entropy of the reservoir is constant, any entropy decreases in A and C must come at the expense of decreasing the amount/strength of correlation between A and C. This, according to the author, means that an entropy decrease in C automatically results in the observer in system A losing any memories or records (a memory/record is a kind of correlation) of C’s previous higher entropy state. However, very little correlation (a very small memory/record) is needed to retain, say, just the numerical values of C’s entropy at different times. Entropy decreases in C could, for all we know, come at the expense of other, more detailed, correlations between A and C, while leaving memories of measured entropies intact. Thus, it seems that much more work is needed to actually establish that entropy decreases are unobservable (due to being impossible to remember). The Phys. Rev. Focus commentary also hints at this problem.