"Doesn't this eliminate the puzzle ? No. If the time-asymmetry of thermodynamics were associated with the Tsymmetry violation displayed by the neutral K meson, then anti-matter would show the reverse of the normal thermodynamic asymmetry. Why ? Because PCT symmetry guarantees that if we replace matter by anti-matter (i.e. reverse P and C) and then view the result in reverse time (i.e., reverse T), physics remains the same. So if we replaced matter by anti-matter but didn't reverse time, any intrinsic temporal arrow or T symmetry violation would reverse its apparent direction. In other words, physicists in anti-matter galaxies nd the opposite violations of T-symmetry in weak interactions to those found in our galaxy. So if the thermodynamic arrow were tied to the T-symmetry violation, it too would have to reverse under such a transformation.

But now we have both an apparent falsehood, and a paradox. There's an apparent falsehood because (of course) we don't think that anti-matter behaves anti-thermodynamically. We expect stars in anti-matter galaxies to radiate just like our own sun (as the very idea of an anti-matter galaxy requires, in fact). And there's a paradox, because if this were the right story, what would happen to particles which are their own anti-particles, such as photons ? They would have to behave both thermodynamically and anti-thermodynamically!"