Great idea Redcrown.
I just did the same thing with an L* image I'm working on in Topaz Studio. This image is not as broad spectrum as Andrew's test file, but is entirely within the L* gamut (as can be seen in the Colorthink pic attached).
First I duped the layer, then ran the duplicate through Topaz Studio doing absolutely nothing but saving immediately upon arrival. Looking at the resulting difference layer and the histogram statistics there was a standard deviation of 0.31 and a mean of .11.
Then I opened a separate file in the stand alone version of Topaz Studio. I did nothing but save it as a separate file. I then opened it in Photoshop, converted it to L*, then copied that image as a difference layer together with my original file. There was a standard deviation of 0.32 with a mean of .11.
Then for frame of reference, I converted my L* image into ProPhoto, saved it, then converted it back into L*, copied it as a difference layer into the original L* layer file. The standard deviation was .03 with a mean of .00.
So something is going on when using Topaz that's now completely inexplicable to me. Maybe there's a conversion into some other workspace. I really like what Topaz can do, but I wish i understood a bit more about all this as merely opening it up appears to be more consequential than a colorspace conversion, at least for my test file which admittedly is hardly a comprehensive test.
I noticed that saving the file separately using Topaz's stand alone version of Studio that I was given the choices of saving in only ProPhoto, sRGB or ".TSP" format. TSP appears to be an extension used by Topaz so that if you save in it, you open back up the existing project in its current state. See
https://help.topazlabs.com/hc/en-us/articles/115001574951-Project-Files-tsp-.
So now it's more a mystery at least to me.