POWERSHIFT said:
If the universe was infinite, wouldn't it, according to the 2nd Law of Thermodynamics, have no heat? And if it isn't infinite, that means it's finite, and thus had a beginning. Which also means time had a "beginning." So to speak
That is a famous arguments from the creationists, they say that (acc. to physics) the world needed to have a beginning, based on the 2nd law of Thermodynamics. However, their idea clearly contradicts the 1st law of Thermodynamics, which claims that the total quantity of energy in any system, is constant, and thus no creation or destruction of energy is possible.
The issue onhand is however much more complicated. Based on E=mc^2 the 1st law of Thermodynamics we need first to consider physical matter too, so the total quantity of both physical matter (mass) and energy is a constant.
Second, both laws of Thermodynamics were originally constrained to laboratory scale thermodynamic systems which were closed and had a thermodynamic boundary. The 1st law (in it's contemporary form, based on GR and QM) still holds for all systems, including the universe. Physical matter creation, as what happened on a mass-scale in the early universe, does not contradict that, because it was a conversion of energy in another form.
The problem with the 2nd law of Thermodynamics however is that it is still constrained to thermodynamic systems which have a thermodynamic boundary.
This does not apply directly to the universe, because apart from the cosmological issue of open or closed universe, there is in the strict sense no thermodynamic boundary to the universe. There's no border or boundary to the universe (cosmological principle), and that is true even when the universe turns out to be a multiversum.
In the Thermodynamic sense the observable universe is an open system, since it does not have a boundary and is in thermal contact with the rest of the universe, beyond our horizon.
For the universe in total the terms open or close with respect to it's Thermodynamic behaviour makes no sense since there is no boundary to the "rest of the universe" (since the total universe already encompasses that) so that it is neither open nor closed.
But there is also something else peculiar about the universe. You might have seen these pictures of a sequence of moments of time in which a gas in a container spread outs through the container (due to entropy or the 2nd law of TD) and becomes uniformly spread through the container.
At the microscopic level however, all physical laws work both ways, so how do we know the progress of time? When we have to order the pictures (let's say there are 3 pictures, one with local concentration(s) of molecules, the next with a medium spread of those molecules in the container but not yet uniform, and the third a uniform distribution) we would clearly say that the progress of time is from picture 1 to 2 to 3.
Yet, when this picture was not of a small gass container, but was of cosmological size, we would need to arrange the pictures in the opposite order! Due to gravity, local matter clumbs together forming stars, galaxies and clusters of galaxies.
So if we were not told what scale the picture represent or that the scale is a varying quantity, we could not say what the right direction of time was!
In the example of the cosmological progress of distribution of matter, there are two important differences with the example of the small gas container. First, the progress of time is from a uniform distribution towards local clutterling of matter, forming galaxies, stars, etc., and the scale of the 'container' grows, due to cosmological expansion.
In terms of entropy, this in fact means that the growing metrics of space allow for more possible states, so this in fact means a lowering of entropy at a cosmological scale!
If you search online, you might find a lecture of Roger Penrose on this issue of cosmological expansion and entropy, which is very interesting.
This is just some basic information, the issue itself is far more complicated as I can explain, but at least I think you get the basic idea that you can not simply scale up our laboratory scale experiment and conclusions based on the 2nd law of Thermodynamics to cosmological scales.
I don't give a proof of it, but one could suspect that on truly cosmological scales (the universe as a whole) the issue of entropy is different as expected, and might lead to the conclusion that entropy is a conserved quantity throughout the cosmos, even if at local scales the 2nd law still applies.
But perhaps someone else more educated on this subject can explain more details.