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Is there a way to send only one program to sleep mode (in this case mathematica on linux) and keep the rest of the operating system alive?
Try suspending the program:
kill -TSTP $PID suspends the process
kill -TSTP $PID
kill -CONT $PID resumes it (source)
kill -CONT $PID
You can lookup $PID in ps -Al.
Required, but never shown