There's a widely acknowledged problem involving the Second Law of Thermodynamics. The problem stems from the fact that all known fundamental laws of physics are invariant under time reversal (well, invariant under CPT, to be more accurate) while the Second Law (a non-fundamental law) is not. Now, why is the symmetry at the fundamental level regarded as being in tension with the asymmetry at the non-fundamental level? It is not true that solutions to symmetric equations must generically share those same symmetries. In fact, the opposite is true. It can be proved that generic solutions of systems of partial differential equations have fewer symmetries than the equations. So it's not like we should expect that a generic universe describable by time-reversal symmetric laws will also be time-reversal symmetric at every level of description. So what's the source of the worry then?

I think it comes from a commitment to nomic reductionism. The Second Law is, well, a law. But if you really believe that laws are rules, there is no room for autonomous laws at non-fundamental levels of description. The law-likeness, or "ruliness", of any such law must really stem from the fundamental laws. Otherwise you have overdetermination of physical behavior. Here's a rhetorical question taken from a paper on the problem: "What grounds the lawfulness of entropy increase, if not the underlying dynamical laws, the laws governing the world's fundamental physical ontology?" The question immediately reveals two assumptions associated with thinking of laws as rules: the lawfulness of a non-fundamental law must be "grounded" in something, and this grounding can only conceivably come from the fundamental laws.

So we get a number of attempts to explain the lawfulness of the Second Law by expanding the set of fundamental laws, Examples include Penrose's Weyl curvature hypothesis and Carroll and Chen's spontaneous eternal inflation model. These hypotheses are constructed specifically to account for lawful entropy increase. Now nobody thinks, "The lawfulness of quantum field theory needs grounding. Can I come up with an elaborate hypothesis whose express purpose is accounting for why it is lawful?" (EDIT: Bad example. See this comment) The lawfulness of fundamental laws is not seen as requiring grounding in the same way as non-fundamental laws. If you think of laws as descriptions rather than rules, this starts to look like an unjustified double standard. Why would macroscopic patterns require grounding in a way that microscopic patterns do not?

I can't fully convey my own take on the Second Law issue in a comment, but I can give a gist. The truth of the Second Law depends on the particular manner in which we partition phase space into macrostates. For the same microscopic trajectory through phase space, different partitions will deliver different conclusions about entropy. We could partition phase space so that entropy decreases monotonically (for some finite length of time), increases monotonically, or exhibits no monotonic trend. And this is true for any microscopic trajectory through any phase space. So the existence of some partition according to which the Second Law is true is no surprise. What does require explanation is why this is the natural partition. But which partition is natural is explained by our epistemic and causal capacities. The natural macrostates are the ones which group together microstates which said capacities cannot distinguish and separate microstates which they can. So what needs to be explained is why our capacities are structured so as to carve up phase space in a manner that leads to the Second Law. But this is partly a question about us, and it's the sort of question that invites an answer based on an observation selection effect -- something like "Agency is only possible if the system's capacities are structured so as to carve up its environment in this manner." My view is that the asymmetry of the Second Law is a consequence of an asymmetry in agency -- the temporal direction in which agents can form and read reliable records about a system's state must differ from the temporal direction in which an agent's action can alter a system's state. I could say a lot more here but I won't.

The point is that this sort of explanation is very different from the kind that most physicists are pursuing. I'm not saying it's definitely the right tack to pursue, but it is weird to me that it basically hasn't been pursued at all. And I think the reason for that is that it isn't the kind of grounding that the prescriptive viewpoint leads one to demand. So implicit adherence to this viewpoint has in this case led to a promising line of inquiry being largely ignored.