[katieHaylor (OP)]

Donald says:

I know that entropy - the degree of disorder, or randomness in a system - is always increasing. But at what rate?
Is the increase logarithmic, linear, exponential or indeterminate?
Could we calculate entropy by simply scaling up space?

What do you think?

[chiralSPO]

I'm not sure if we can know the overall rate of change in the universe, other than it is positive and nonzero. Some parts of the universe experience decreasing entropy, but those are far outweighed by the parts for which it increases. My guess is that the average increase throughout the universe is likely to be highly skewed by a small number of very extremely entropizing (not sure if that's a word) phenomena.

I think another similar question is, how much entropy did the universe start with?

[jeffreyH]

If conditions before the big bang could be described as a condensate then the entropy would be undefined. Since adding to or removing things from a condensate make no difference to the condensate. However this cannot be considered 'ordered'.

[evan_au]

a small number of very extremely entropizing (not sure if that's a word) phenomena

One of these phenomena is the stars. They burn hydrogen into heat, and heat is one of the most "entropized" end products.
When stars reach the end of their lives, the larger ones collapse in a supernova, which produces more heat than the whole galaxy combined (for a short amount of time).

at what rate?

If I were to try and describe it as a simple function, I would say "negative exponential".

As the universe expands, matter becomes less dense, and less of it is likely to come together to form stars. Much of the remaining matter will end up in black holes (their accretion disks radiating even more heat). Entropy can't increase much when all you have are widely separated black holes.

This leads to the expected heat death of the universe.
See: https://en.wikipedia.org/wiki/Heat_death_of_the_universe