Could one really have the nerve to suggest "retiring" the idea of entropy? (I actually do not believe that we abandon old ideas before new ones are developed. Old ideas disappear, or are modified, only when new better ideas are developed. They are never just retired.) So, no, we should not retire entropy, but perhaps treat it with a little less importance, and recognize the paradox it creates.
Entropy, the measure of the degree of disorder in a system, has held a lofty place in physics, being part of a Law no less (not just a theory). The Second Law of Thermodynamics says that in any closed system entropy always increases with time. Unless work is done to prevent it, a closed system will eventually reach maximum entropy and a state of thermal equilibrium. Max Planck believed that entropy (along with energy) was the most important property of physical systems. Sir Arthur Eddington is quoted as saying that "The law that entropy increases—the second law of thermodynamics—holds, I think, the supreme position among the laws of Nature." But as a young physics student in college I must admit I never understood their excitement (and I was not the only student to be unimpressed). The Second Law seemed of minor importance compared to the First Law of Thermodynamics, the conservation of energy—energy could be transformed into different forms, but it was always conserved. The First Law had beautiful partial differential equations (as did all the conservation equations of physics) whose solutions accurately described and predicted so much of the world, and literally changed all our lives. The Second Law was not a conservation equation and had no beautiful partial differential equations. It wasn't even an equality. Has the idea of entropy and the Second Law had any major affect on science and engineering or changed the world?
The Second Law was a statistical "law", initially a generalization of conclusions reached when looking at the motion of molecules/particles. As students it was easy for us to understand the classic example of how hot (fast moving) molecules on one side of a closed box mixed with cold (slowing moving) molecules on the other side, and why they could not separate again once they were together and all at the same temperature. We understood why it was irreversible. And we understood the concept of the "arrow of time". Sure, the mathematics of the First Law (and the other conservation equations of physics) worked in both directions of time, but with initial conditions and boundary conditions, we always knew which way things moved. It didn't seem to require another Law. In fact, the Second Law (as applied now to all situations) seemed to be an assumption rather than a Law. Especially when it was applied to an entire Universe, that we understand so little about.
When looking at the Universe (whatever that entails, which may be more than our presently visible/observable universe) the First Law tells us that all the energy in the Universe will be conserved, although it may be converted into various forms. But the Second Law says that at some time in the future no more energy transformations can take place. The Universe will reach some stage of maximum entropy and thermal equilibrium. The Second Law essentially says that the Universe must have had a beginning and a end. That is very difficult to accept. The universe must be timeless, for if there was a beginning what was there before this beginning. Something cannot come out of nothing (and by "nothing" I mean the lack of anything, even things we do not know about yet).
Of course, the present Big Bang theory has a beginning (of sorts) and our present form of the universe has apparently expanded out from a singularity, but we do not know what came before that, and oscillating models of the universe are being proposed, so that the Universe is timeless. With such models, if entropy is very high at the end of our universe and was very low at the beginning of our universe, what process could essentially reset entropy to a low value? As relates to an oscillating universe, should entropy perhaps really be conserved somehow? Could there be some type of energy conversion that does not require work (in our classical sense)? Could the Universe actually be the one and only possible perpetual motion machine (forbidden by the Second Law)? If existence is endless in time, it would seem so.
The whole idea of entropy has always felt wrong or misplaced in other ways also. We talk about the Universe going from order to disorder. Yet this supposed order is merely because all the matter of the universe was compressed together in some tiny volume/singularity and when it expanded out there was less order because the particles were more spread out. And yet order is being created all the time.
The greatest result of our expanding and evolving universe is the great and ever increasing complexity that has resulted, first, from gravity condensing matter, then supernova explosions creating higher number elements, then from chemical evolution, and then, most dramatically, from biological evolution (driven by natural selection), culminating in self-reproducing life and eventually the incredible complexity of our brains. Complexity is synonymous with low entropy. The expanding universe has countless small (relative to the size of the universe) pockets of extremely low entropy surrounded by vast areas of higher entropy (much of which resulted from the creation of these low entropy areas). Are the higher orders of complexity (and thus lower orders of entropy) taken into account when trying to balance the entropy of the Universe? There are in fact many scientific papers written today in cosmology trying to sum up the Universe’s total entropy, with formulas that could end up being incrdibly too simple to account for all the (as yet unknown) physics going on in our strange Universe.
We cannot retire entropy, but should we maybe rethink it?