how to log the idle time of user on a remote computer

If your remote machine is windows, then you can use remote wmi to do this. Just google WMI CPU Usage and Remote WMI. WMI is COM - so you'll have to then build some form of bridge from Java to COM. If the remote machine is not Windows - then there are tools out there like good old TOP - but you'll have to then figure out how to get that data back in the way you want.

I suspect the very easiest (maybe not the nicest) is to create a VBScript to monitor the remote machine using WMI and write the result to stdout. Then launch that script via "cscript script.vbs" using the Java something like this:

Process p = Runtime.getRuntime().exec("script scripts.vbs");