A question: The entropy of the universe taken as a whole, modelled as a molecular dynamics system

``Everyone knows'' that the entropy of the universe, taken as a whole, increases.

Suppose that we model the entire universe (i.e. the entirety of the known physical universe) as a huge isolated system, using molecular dynamics (MD for short).

The question is: How would you show that the entropy of such a system does in fact always increase? that it neither decreases nor stays the same? Is it even possible to show it, using MD?

Notes:

Assume infinite space (or at least a sufficiently large space that never falls short in simulation, may be with some technique for on-the-fly extension of space).

Treatments such as https://doi.org/10.1063/1.1636153 do not address the above question. Neither does the answer in this Physics StackExchange thread: https://physics.stackexchange.com/questions/360487/computing-entropy-pro... Both deal with a finite portion of the universe, and not with the universe taken as a whole.

Notice that in MD simulations, heat exists only in the form of the motion of the molecules (particles).

I thought of raising this question because I thought of a certain ontological-physical principle which I thought was necessary, and so, should be mentioned in such discussions, but didn't find it mentioned. However, before giving my thoughts, I would like to see whether this principle is really necessary, or is it a false indicator (i.e., a wrong way of thinking about this issue). BTW, what I had in mind here was a very simple observation, not a big principle as such. It doesn't change the existing theory or maths; I was only trying to figure out how the theory might be applied. The interest is only limited to conceptual clarity.

See if it interests any one.

Best,

--Ajit

 Updated a bit after posting at 2024.03.20 18:25 IST.