How do irreversible processes relate to entropy on a microscopic scale? I'm having trouble visualizing this on a universal scale.
Irreversible processes involve changes that can't be undone (go in reverse) as easily as they happened forwards, which is equivalent to saying that they increase the entropy of the system and its environment.
Microscopically, this happens when the process transforms energy (ultimately) into heat, instead of purely between potential energy. Conversion to thermal energy can increase entropy for two reasons: one is that each particle in the system may gain more units of thermal energy, which increases the number of microstates of the system. For analogy, if I have a bunch of boxes (representing particles), then the entropy of that system of boxes is a minimum because there is no additional information for which box contains. But if I add some marbles to them (representing units of energy), then the entropy increases because now there is additional information about how many marbles are in each box.
Another way that conversion to heat can increase the entropy is that the heat may be radiated to the environment, which increases the number of microstates since then there are photons to account for, or vibrations in surrounding molecules if the transfer involves conduction or convection.
Macroscopic examples include exothermic chemical reactions, or the plastic deformation of a structure (as opposed to elastic deformation). Another good example is friction vs. frictionless movement.
Cosmologically, the expansion doesn't change entropy for two reasons. First, because the expansion is adiabatic (by definition). No thermal energy is lost to the surroundings because there are no surroundings. The second condition is that the expansion doesn't rearrange the distribution of internal energy or matter. This is
unlike the free expansion of a gas to fill a container, because the container originally has information about what bits of volume within it contain atoms or not. Free expansion of a gas to fill the container leads to more microstates being occupied, but the expansion of the universe does not lead to occupying more microstates. The universe is not filling in an originally empty space as it expands!
So instead of the entropy of the universe increasing by expansion, it increases
only because of irreversible processes happening within -- stars forming, black holes growing, life evolving and doing its thing, and so forth. This is what I wanted to emphasize after your description of the universe's increasing entropy. It isn't because of expansion. It's completely independent of expansion! We cannot use the free expansion of a gas as an analogy for it.
Wat if the entropy of a black hole relates to its surface area, may that indicate that our universe can be described as existing on the surface of a black hole?
Not
literally, but describing it that way can lead to some useful insights about the nature of information and spacetime. PBS Spacetime has some good description -- I'll refer to them.
[youtube]klpDHn8viX8[/youtube]