When T is 1000 you can get the blue to 0.98 of what red was initially… so I imagine in the infinite limit you can get all the way there.
This seemed weird to me, so I looked at the final temperature distribution of all of the n blue blobs, as n increases. I’ve plotted them here (blue lines have n being small; red lines have n being big). You can see that as the number of blobs becomes very big, the fraction which have temperature less than 1 falls… (i.e. knee of graph moves to the right...)
Having checked this, you’re totally correct.
Here’s a short Python program that checks this empirically.
A graph of the scaling of the max blue temperature with respect to number of divisions is here:
https://imgur.com/a/r4hdaJD
When T is 1000 you can get the blue to 0.98 of what red was initially… so I imagine in the infinite limit you can get all the way there.
This seemed weird to me, so I looked at the final temperature distribution of all of the n blue blobs, as n increases. I’ve plotted them here (blue lines have n being small; red lines have n being big). You can see that as the number of blobs becomes very big, the fraction which have temperature less than 1 falls… (i.e. knee of graph moves to the right...)