Qt has no classes that influence other applications directly. I think the easiest way to do what you want is to rebuild this other application with dbus or shared memory facilities that will inform its environment that the state of the application has just changed. You will have to code both sides of this mechanism though. An alternative is to use XEmbed to embed the window of the ebook reader into your application (then you will know when it is minimized or maximized) or to hook into X11 event system and intercept appropriate messages sent by the window manager to the application in question.
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