The Second Law of thermodynamics states that "The entropy of a closed system cannot decrease over time."
What are the philosophical implications of this statement, especially wrt to theology and metaphysics?
I don't think there are many implications.
For theology, you're usually assuming that the system isn't closed. So the 2nd law doesn't apply.
If you want your metaphysics to be consistent with the second law, you are not allowed to assume something that would lead to less-than-zero entropy far in the past. You could decide that the universe is an adiabatic reversible process (entropy = constant), or that it approaches adiabatic reversibility as you go further back in time. You could postulate that there was some time in the past where the rules changed or things started. Or you could devise a scheme where the system isn't closed, or assume that it's infinite (i.e. you can in principle push your entropy away to infinity to have whatever local entropy you like). Since you only need at least one of these to be true for the 2nd law to not be problematic, you have a lot of wiggle room.
Thus, although the second law is an extremely important principle in physics, it's pretty inert philosophically.
Since by re-arranging your furniture or physically exerting any action you convert energy (you got from food) into work. The energy is the movement of the physical action.
Taking the 1st law of thermodynamics into account: energy can neither be created or destroyed you could also say it is continuously converted. The entropy as I understand it is the state of energy converted as work, so it can be concentrated (a bit like a dense bundle- or that extra strong shift of the heavy sofa) or scattered (like droplets or particles-re arranging the ornaments into position for example) which ever 'state' the energy remains the same expressed in work (concentrated on one big lift or scattered over duration across smaller items).
Any conversion as an action has a duration (time) and every action converts potential energy into work, increasing the entropy from the last action of conversion.
Applying this to humans (and theology is a human logos) you could interpret this that every action has a consequence between human beings. The action can be physical interaction and communication of information, opinion, ideas, concerns, etc...This would imply that humans all shape through the conversion of energy into work their world (natural and intangible) and I guess makes a case in theological and philosophical terms that the individual is a spec in the wider picture we call existence and 'reality'-and hence places responsibility onto each individual in being through action (existential philosophy: Heidegger on 'Dasein'.
The entropy in this case with an ever growing world population (and hence increasing conversion of existing energy into work) over time can only increase, which can be a bit disconcerting as it implies increase in diversity and quantity (difficult to control and bundle) some may call 'chaos' (Greek creation mythology: Chaos). On the other hand if you flip this the other way round and think what would therefore decrease entropy you come up with a nihilistic solution of self extinction we currently witness through the actions of terrorists.
Baring in mind that the potential energy released at the beginning of time which formed the Universe (and in a truly macroscopic system that started with scientifically called the 'Big Bang', or 'Chaos' in mythology, God as the creator in Christian believes, etc...), and eventually our planet, life, on the 1st law of thermodynamics will always remain the same and the system (the Universe, planet Earth) would not be any worse off just differently transitioning and manifesting- if we as a species are no longer around.
So this means that it is very much in our own interest to sustaining ourselves, others and our World. The increase of entropy is inevitable, we should not focus on wasting our energy on changing and controlling this energy but 'go with the flow', more akin to non material existence as encountered in Eastern Philosophies and Religions, such as Taoism and Buddhism, Hinduism- or to decrease-go back in time.
A funny answer is to remark that living things have to keep lowering their entropy for them to live (thus giving at least the same counter part to somebody else). If they did not, then they would reach a state of equilibrium, and as we all know, life is clearly not an equilibrium state. This is quite surprising, because life is recent in the history of the universe, while second principle of thermodynamic make us want to believe that the universe is getting closer and closer to its global equilibrium state.
How comes then, that "complex life" as us took so many times to emerge, if second law seems to go against it? Well, quite simply: their must exist some place in the universe that contains all the entropy required for living being to be, and complex structures to emerge. What are these places? They are our famous black holes. Black holes are the biggest well of entropy in the universe, and they took times to emerge. This is why, even though the second law of the universe seems to imply that the universe is getting more and more smooth and structureless, the existence of black holes allows him to actually complexify, even to make life a sustainable state of existence.
Conclusion: the second law of thermodynamics is against life, but the existence of black hole is here to sustain it. So, are black hole also here to allow complex structures to emerge in the universe (even life), or is it just a coincidence?
While I find "Rex Kerr's" answer quite nice, clear, and a bit startling, it seems to apply to a "big box" picture of some sort of "completed" metaphysical system. I am not sure one could refute a metaphysics simply by inconsistency with the Second Law, since its meaning remains unclear. Even in physics, Boltzmann's equation seems more like a mathematical "truce" than an ontological clincher. Assuming there is a role in our metaphysics for some sort of temporal consciousness or "Sein und Zeit," etc., we have innumerable issues raised by the Second Law. These assume their most compelling form in Maxwell's Demon, which I believe even Maxwell presented as a puzzler dealing with the nature of "mind" or "mental work." I am not competent to assess the various models of the demon proposed over the years. But I believe the most intriguing, in relation to res cogitans, is the one offered by Landauer, in which the demon can indeed reverse entropy in its little world as long as it can keep "remembering" what it defines as order, even as that order changes. As long as it can still "tell the difference." The problem comes with memory storage, the demon's "historical" account, so to speak. At some point it must physically clear or erase its memory. And this, as Landauer shows, is what requires external energy, more energy than the demon's efforts can conserve. The vague resemblance between the demon and the transcendental subject is intriguing. So how exactly does this impact metaphysics? Um, I'll get back to you in a few years, if I can remember how.
For an extensive discussion, with extensive citations, of the cultural, philosophical, and religious implications of the Second Law, see the book Entropic Creation: Religious Contexts of Thermodynamics and Cosmology by Helge S. Kragh.
A lot of the implications one draws from this are going to depend on one's underlying metaphysical assumptions, and how one defines the key terms "entropy" and "information".
The Second Law, as you state it, is trivially false; if I take my living room to be a closed system, I can decrease the entropy there by organizing things and imposing order. In fact, viewed this way, humanity represents (in a metaphysical or theological manner) the pinnacle of the negentropic principle.
For this reason, most scientific views of thermodynamics tend to focus on the microscopic dispersion of energy, and not effects at the macroscopic level.