I am a biologist and very recently there has been a movement to increase the use of preprints in publishing biological research. This has generated a lot of discussion about preprints and their merits and has spawned a few servers (e.g., bioRxiv) but I have not gotten a good sense of how I should incorporate the preprint server into my normal publishing workflow.
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This is really a question for academia.se, but you're right that the arXiv is used primarily by physicists (along with mathematicians), so I'll answer it here so you don't feel the time was wasted.
The role that pre-prints have in the collective workflow of people in a field depends half on each person's preferences and half on how it gets established as a means of communications. There are no 'right' or 'wrong' workflows for using a pre-print server (though there are wrong ways to use one), and you should use the one that fits you best personally and lets you communicate best with your colleagues.
There is a broad spectrum of reasons you might want to upload a preprint, which are explained in detail in this question. To give a brief summary, you might upload a preprint or postprint
or for many other reasons. Whether these (or others) apply to you will determine how you use the repository. Some of these are personal choices, and may come down to how much you feel you stand to gain from non-institutional readers having access to your work. Some of these are field-dependent, and hinge on there being a significant fraction of the workers in your field that regularly check the repository.
The appropriate time to upload will typically vary on a case-by-case basis. You might upload at an almost-finished stage, at the time of submission to a journal, at time of acceptance, at the time the paper is published, or even six to twelve months after that. Each of these corresponds to some or other of the motivations above.
One thing that's important to keep in mind is that you must have a good idea of prospective journals you'd like to publish in, and of what their preprint policies are, before you upload, as it can rule out certain publication venues if you're not careful. This is again field-dependent; many physics journals take that as standard but biology ones might not.
Workflow may be different, but the one I am familiar with is:
Sometimes version on arXiv is put before the submission to a journal, for example:
And in some cases, arXiv is used instead of a journal, especially if: