Either use named pipes which would be the fastest way or use Sockets to exchange information between two .NET processes. However in your case it would probably be simpler you write the information to a file and let Unity read that file.
There’s no easy way to get the string in the memory space of one app from another app.
I would say it would be probably easier to find a better solution that have 2 different apps communicate with each other (e.g: use a native plugin that retrieves this value).
NOTE: this approach would not work on all platforms of course.
You can achieve this in many different ways (See this 1 for more information on Inter Process Communication).
The easiest way it would be to have the external app report the CPU id value to the console, and have the game execute that app and read its output.
The game would parse the output from your external process and read the value (multiple values can be reported that way, as long as both apps agree on a common structure of what is being output and how to read it).