(Please bear with me if this is a stupid question; I'm not a physicist, just a curious student.)
I know that Noether's Theorem links symmetries to conserved quantities: the fact that the laws of physics work anywhere in space, for example, is linked to conservation of linear momentum.
In particular, if the direction of time were reversed (we replaced all the $t$s with $-t$s), we would have a "conservation of entropy". But the second law of thermodynamics says that entropy isn't conserved. Therefore, the laws of physics aren't symmetric under time-reversal.
This seems strange, because the laws of physics are symmetric under time-translation (this gets us conservation of energy, which does seem to be true).
So my question is: what law of physics breaks under time-reversal that doesn't break under time-translation?