PDF preview on other monitor

While Adobe Reader has a beautiful rendering, you might prefer a different PDF viewer for previewing. If you have a PDF viewer in a separate window, that reloads the PDF without closing and reopening, it is easy. You can just drag it to the other monitor once and it will stay there while refreshing. I use SumatraPDF, which supports this kind of silent refresh. It also doesn't lock the PDF file and offers the possibility to jump back to the right place in source code by clicking in the PDF (SyncTeX, cf. forward-inverse-search). I used Texmaker and its forks this way under Windows. You can refresh the pdf manually with r or let your GUI refresh it via command line as soon as the compilation of the PDF to review has finished.

Additionally to SumatraPDF as an external PDF viewer, which can be called from any GUI, there is at least one fork of Texmaker that offers a PDF preview window without external tools, with all the possibilities I mentioned above. Maybe it's TeXstudio.

Maybe you have to deal with the focus of SumatraPDF and decide if it should stay at your TeX GUI window or change to the external PDF viewer window.

With newer versions of Texmaker (>4.5) the built-in viewer can be detached and moved to another screen. Via Options -> Configure Texmaker just untick the Embed (marked in image) in the "Pdf Viewer" section.

I don't know about Texmaker, but on Windows, you can achieve this with SublimeText2 as an editor, associated with its plugin LaTeXTools and SumatraPDF as a viewer.

You can keep the viewer window opened (on any monitor) and it will be updated each time a new compilation succeeds. You will be able to do forward and inverse search.