I have a music file that is shorter than one second and whenever I save it as mp3, there is always empty space to make it bigger. I'm assuming there's a minimum for mp3. I'm using Logic Pro X. Anyways, how can I do this?
I have just done a few experiments using Audacity running under Linux.
I created an mp3 file of length one second, which saved as a file of size 17729 bytes which opens as a 1 second audio file. After cutting it in half (in Audacity) and saving (technically: exporting) it, I get a file of size 9370 bytes which opens as a 0.5 second audio file.
So, I believe that any problem you are having is due to the software you are using, an not due to some limitation of the mp3 file format.
Further experiments with 0.25 seconds and 0.1 seconds produce ever smaller file sizes. There will be a minimum, due to the embedded mp3 tags in the file.