Photo loosing sharpness when passing it to Photoshop and viewing it in LR again

Question

Hi
I passed a JPG from LR to Photoshop CC, did a little change and saved it. Then I realized, that the PSD file has lost some sharpness compared to the original JPG.
It doesn't matter if I pass it with the option "with lightroom changes" or not. It happens in both cases that use a copy.
That's really weird and frustrating.
But, I found out that this only the case if I view the photo in LR   (In Phothoshop and Irfanview all version of the photo looks the same regarding the sharpness)
A very ugly bug in LR 5.7?
edit:
The difference get smaller after viewing both photos in 1:1. But still, there is a difference viewable when switching between exactly the same images (just passed it for test purpose to Photoshop as copy, and saved it as JPG, no editing in PS).
Regards

Answer 1

First of all I should say that I was able to download the file, but initially I got an error that said it was not found.  It was probably just an incompatibility of the dropfiles site and my default browser download plug-in and it finally worked just using the standard browser download function.  Looking at the contents of the photo, itself, there are no LR adjustments that have been saved to the JPG, only a few metadata changes such as adding the photo location as being in Hawaii.
Anyway, there are several issues that are being mixed together:
1)  When a JPG is opened and resaved it will be slightly different due to JPG compression being a lossy format and that the color workspace in PS is slightly different than in LR so when PS converts the colors from its 16-bit workspace to 8-bits the output pixels won't be exactly the same as the input pixels even if there were no substantive changes in PS, just an open and resave.
In this 4:1 screenshot the PS photo does have more variation in colors between adjacent rows of pixels than the original in LR:
2)  This variation in colors can lead to an apparent difference in sharpness in LR when a resampled-smaller zoom level is used--in this case Fill with a small LR window size:
3a)  The PS resampling for display and the LR resampling for display use different algorithms due to LR having to be as quick as possible, so what you see at those zoom levels doesn't accurately reflect the actual image sharpness, only resampling algorithm accuracy and differences.
3b)  In LR there is a warning badge in the Detail panel when using zoom less than 100%.  Unfortunately the warning disappears when I press a key to do a screen capture of it:
So to summarize, pixels don't remain unchanged across an Open/Save cycle when you're using the lossy JPG format -- a reason to use TIFs, and less than 100%/1:1 zoom levels don't show sharpening accurately in any program and differences between resampling algorithms in different programs result in differences in the inaccuracy of the resampled result.  In other words, with less than 100%/1:1 zoom PS's inaccuracy is different than LR's inaccuracy so neither should be used to judge sharpness, and you should use 100%/1:1 zoom or higher.