The laws of thermodynamics aren't actually laws. They're correlations.
What exactly do you mean with this? The conservation of energy (first law of thermodynamics) is quite a law. Maybe you could say that the second law of thermodynamics is a principle or a statistical corollary. Better said: The increse of entropy happens because of the emergence of a statistical property that is accounted for by multiple interactions that follow the laws of physics (it is a statistical emergent property of the interaction of particles as dictated by Newton's laws of motion, for example). So yeah in that sense the second law doesn't add anything about fundamental physics since its an emergent property and its behaviour also exhibits emergence from simplier (more fundamental) rules (laws of nature), you are just observing the collective action of newton's laws (for example) in a complex many-component system. But this is missleading because the second law tells something more than what statistics tell about interacting particles in a newtonian framework (just to follow the same example): it tells us that the universe had low entropy in the begining, it tells us that the universe didn't started as a thermal soup but as a highly ordered state that has been degrading over eons and will for much more. So it can't be just a principle clearly (nor a "correlation").
Mr. Missed Her:
Hey, what if you tried to reverse entropy by surrounding Earth with infra-red sensitive solar panels? (Let's assume that Earth has been teleported into the middle of a big void, because the Sun's march towards entropy is keeping entropy at bay here.) The solar panels would convert all Earth's radiated heat to usable energy, which could be stored in batteries. There would then be much lower entropy than before Earth cooled off. So, what would stop me from breaking the second law of thermodynamics?
You have assumed that "The solar panels would convert
all Earth's radiated heat to usable energy" this is a supposition that breaks the second law. You are assuming a situation where the second law can be broken to demonstrate that the second law could be violated as a conclusion. If your conclusion is your premise then a self-contained circular reasoning has taken place, a circular reasoning independ and isolated from the real physics, therefore coherent in a sense even if detached from nature and its principles.
So your model doesn't work in reality because you never took into account the rules of nature in the first place. But if the question you are asking is really what impedes you from recycling all the energy with the solar panels - battery system then the answer is more complicated.
1) The 100% of the energy radiated from Earth can't be absorbed entirely by any "inert" device.
2) The 100% of the energy absorbed by the solar panels can't be stored in the chemical battery
3) The 100% of the energy stored in the battery can't be retrieved from it
4) The 100% of the retrieved energy from the battery can't be converted into usefull work without the need of an external source to the entire system.
All of these 4 points are not technical challenges that could be overcomed in hypothetical engineering breakthroughs but are consecuences of the second law. Each one of them.
For me is hard to explain in a clever way the step-by-step logical path from the second law to 1), 2) or 3) but I can see inmediatelly why the fourth is impossible (and therefore even if 1), 2) and 3) were overcomed you still couln't transform the 100% of radiated energy to usefull work since 4) would still hold).
Instead of the battery think about ina more general sense; think about any device that can store energy that then can be retrieved by plugging something into it or opening a valve or something. In this sense the battery is no different than a dam. You can store energy in a dam accumulating water on one side. The water level will rise until you fill the battery (fill the dam), and thus there's now a lot of mass at different heights to the top of the water. This means there is potential energy. So you have stored potential energy in this dam, the same you can store chemical potential energy in an electric battery. Now suppose you want to take energy from your repository and transform it into usefull work. Easy bussiness, you open a gate in the dam and while the potential energy stored leaks into kinetic energy (in harmony with the mass of water leaking through the gate) you profit from that kinetic energy of the water to pull the blades of a fan and then with gears and things like that you get your usefull work done (it could turn on a machine for breaking bricks, a mechanical computer, anything...).
Great, now: suppose that you when the water has transfered all the kinetic energy you wanted to the blades you think I should use it again, I should store the water in the top of the lake at the other side of the dam. The problem is that you require to lift the water from the ground against the gravitational dwell of Earth, or putted in another way, you have to inject energy into the water and store it as potential energy once again. So you need energy or work to do this. But you are clever and think "if the only goal of my water driven engine is moving the water to the top of the dam again I don't need an external energy source! I could use the energy from the dam to lift the water again inside the dam". This is perpetual motion. Notice that this doesn't violate the first law of thermodynamics (energy is conserved, no new energy is created, it is the same of the dam recycled to perform the job of re-storing the same energy), but as we are going to see it violates the second law. A bit of heat is realeased when the blades are pushed by the water, a bit of heat is released when the engine starts lifting the water again into the dam, a bit of heat is released when the door of the dam is opened, all this energy is been unused, we are loosing energy in all the steps of this "perpetual fountain". But hey! you might think we could make a robot follow the heat and take those crazy moving molecules to make them collide with little gears in a directed fashing and transform that heat into work (so 100% of the energy is reorganized into work), right? NO, the robot needs energy to perform this complex task, even the most efficient robot (no leaks of energy while working) is going to spend more energy in doing this work than the energy he can gathers from heat for a directed purpose. That is more energy than the one of the dam to make all the energy of it usefull, therefore you need to introduce an external source of energy (another dam to power the robot?).
A robot is an active device so its easy to see the problem here but what about "a passive device"? A thermal insulator atached to the leaks of heat in all the machinery could absorb the heat, like your universal solar panels, right? NO. The problem is that even if it can absorb all the heat (maybe putting more solar panels behind that absorb the small leaks from the first layer of solar panels?) the way it is transformed into work can never archive 100% efficiency once again. Why? heat gets released also from the solar panels (since they get hotter)--> suppose no!---> its the same: since you want to make usefull work from that heat perfectly trapped in your solar panels you have to make for example a steam engine with all that collected heat. Microscopic zoom!!!! now each crazy moving particle (heat trapped in the panels) has to push the water molecules with all the violence as to get them in a vapour state so steam can flow and power whatever you want to power with the, remind, leaked heat from the energy recycling process. In this collision heated particles with water many water molecules are going to aquire the energy of the others but also in the mean time the water molecules can bring part of their energy to the heated particles. More of this is expected while water and thermal insulator archive an equilibrium temperature, when this moment arrive you have your steam but you still have a lot of heat in the insulator that can't be estracted because the water is to hot now to absorb the heat from the other. Well you might think again---> let's change this water with cold water again (usign the fountain so its all self-contained) so the water can absorb the heat that the warmed water can't and is still in the thermal absorbant / solar panels- thing.---->Great!! but you still arrive at another equilibrium and now you have to change the water again to extract the tiniest piece of heat still trapped in your anti-heat-leakage device... So in the end you are constantly changing the water to extract work from every time more infinitessimal amounts of heat that are been leaked, this constant change of water requires energy, where are you going to take that energy? from outside is the only answer left.
No matter what you do, the energy gets dispersed or allocated in containers that can't release all of that energy again to perform some work, or better said: they can, but to do that you need more energy than the one you have in your closed system. The dam needs a river repletishing the energy lost, the battery needs to restore it's chemical potentials (even if you can recharge it forever) etc...
But hey, you might say once again---> you are supposing leaks of heat (even if you are trying to patch them with increasing rigour and compelx devices that need energy). What of we conceive a device that can make it without heat leaks!!?---> nice then entropy would stay constant in your ideal, immaginary world, an entropy decrease wouls still be impossible, you just reduced the rate at which entropy increases to cero, but you didn't reduced entropy (just the rate of change). In fact the rigorous statement of the second law is that entropy stays the same or increases but never decreases even in ideal mathematical worlds. And have in mind the fact that besides this reality is still worse (entropy always increase in nature) because even if you leak an infinitessimal amount of heat the fact that the cycle repeats dooms us all, that leaking would end in a soup of energy that can't be used for nothing at all, your engine would stop, your dam wouldn't change level etc...
In your model it would happen the same. Analogous examples can be done for each part of this story but with the devices you described in your model. In the end all would stop, even if your efficiency in 100%.