Problem is that they're looking for a solution to a problem that has no solution. Short of being able to create energy out of nowhere and nothing or make an actual perpetuum mobile or create or move to an entirely new multiverse, it is impossible to stop or escape entropy and the heat death of the universe. It's like a human desperately looking for the solution to the question of: "how do I turn into a Tyrannosaurus rex before I die?". It's just not possible.
Technically, the laws of thermodynamics are postulates that are well-tested; they are not actually fundamentally required to be true. However, logically, the Third Law would serve as a backstop against saying they're inherently false.
But, if one could find that going outside our current box, there is a literally infinite pool of energy? Yay! We won! We may not technically be breaking Laws 1 and 2, but we don't care anymore because we have as much energy as we want to tap!
FTL is impossible. All evidence points to the complete and total impossibility of anything ever moving faster than light. It simply can't be done.
Leaving aside warp drive (mentioned by Laurelin in the quote below), the "all evidence points to" argument is decent, but not ultimately persuasive, since we're talking about cutting-edge research wherein we have very little certainty. By our best model (the one Einstein came up with), technically matter can go faster than light. By definition, particles doing this are called "Tachyons." (If you hear that term in sci-fi, they're probably using it wrong; all it means is "FTL particles.")
The actual relativity equations only state that particles with mass cannot move at precisely
c, and that particles without mass (which will always, always, always be photons)
must move at precisely
c. There is nothing technically preventing the existence of massive tachyons.
Though you're right: experimental evidence thus far has failed to demonstrate that any actually exist.
(Similarly, there is nothing inherently preventing magnetic monopoles from existing, but we've yet to find any, nor figure out how to create them. So that particular one of Maxwell's Laws remains useful in the physical world.)
FTL is impossible in that you can't exceed 300.000km/s, but even then science admits that in theory you can work around this if you contract the space-time so that you're "technically" crossing it faster than lightspeed would allow. Basically, sort of what Vista can do with her powers. The problem is creating something that can actually do that in practice. But it's still possible in theory.
That's still far removed from "make something out of literally nothing".
The Laws of Thermodynamics are postulates based on observation. There is nothing that has proven it's impossible to make something from nothing; all we know is that we've yet to find a way, and people have been looking for a long time.
Something most people don't realize is that the Speed of Light is not some arbitrary value, rather it's the concept that causality itself has a maximum propagation rate. Imagine you had a button and a light, where regardless of where you place the button or light, the light illuminates if and only if the button is pressed. According to physics, if the button and light are one light year apart from each other, the light will illuminate exactly one year after the button is pressed.
tl,dr: While there are some ways FTL may be possible, the sheer condition of having a piece of information end up a light year away less than a year after it was "transmited" would break just about everything we know about causality. And probably make Thermodynamics throw even more of a fit.
Eh... this argument doesn't really hold water. I've seen it made several times, trying to root it in various other ways of looking at the relativity equations and experimental evidence, but the fact remains that this is only true if you insist that causality must be transmitted via light. Which is a circular argument.
Doing the math using Lorentz transforms and hypothetical tachyonic message-carrying particles, you can actually maintain meaningful causality if you limit the speed of message-carrying particles to something based on an equation I solved once, but too long ago to remember the result precisely. (I think I only solved it for two reference frames moving away from each other, rather than also for two frames moving towards each other, which makes me doubt the universality of my result, but IIRC it was 2x the difference of the relative velocity of the ships compared to the speed of light above the speed of light. Which...sorry, that's probably a mouthful and confusing to read.)
The nutshell version is that there is a speed of tachyon-messenger at which message transmission appears to the sender to arrive simultaneously with when he would observe the time-dilated sender to have sent it. As long as the messages travel no faster than that, simultaneity is never exceeded. i.e., you never see a message before you could have sent the message to which it's responding.
Now, unlike
c, this is not a constant, but is instead dependent on the relative velocities of the reference frames. ...unless I'm misremembering and it's a nice neat number like 2
c, though I doubt I'd have forgotten something that neat.
But anyway, causality only starts to get weird if messages can travel faster than that. So one hypothesis that still doesn't allow causality-violation would be that no message transmitted via a carrier particle can be received and decoded faster than this. (That actually is one of the current theories for how light speed remains the maximum info-transmission speed, despite there being demonstrable conceptual objects that can exceed light speed in motion. "Conceptual" because they're usually taking the form of observable and continuous existences but have no real tangible manifestation other than as an absence of other manifestations. e.g. the radiation beam of a pulsar, which can be detected at two places many light years apart as appearing at one with a delay of far less than many years after the other saw it.)
And all of that is just hypothesizing based on a postulate that causality as we know it is immutable and accurate. That was already made wobbly by relativity. It may well turn out that our universe is even stranger than we thought, and that, yes, tachyonic antitelephones enabling messages to be sent into the past are possible. But what the consequences of that would actually look like is entirely the realm of speculative sci-fi at this point.