Unnecessary interruptions is a pet peeve of mine, a single phonecall or email can cost me and my team about 15/30 minutes depending on how long it takes us to deal with the issue and then get 'into the groove' of whatever it was we were doing. There have been specific studies into just how negatively programmers are affected by interruptions and our team used one by Chris Parnin to persuade management that a change in culture was necessary.
The problem is by no means limited to those in development either, a UCL study showed that learning, specifically the ability to retain information, is detrimentally affected by multitasking. If you're reading emails whilst you are doing something that you ought to be committing to memory e.g. whilst in a meeting, reading or reviewing documentation etc. your brain is going to struggle. Tetard's theory on the Fragmentation of Working Time has an interesting diagram that shows a disruption and recovery model that is applicable to any role and shows the productive time lost as a result in a simple format.
My team all have an auto respond on our email;
Thank you for your email.
In order to provide quality output and productivity please note that the development team review and respond to emails between the hours of 9:30 and 10:00 and 16:30 and 17:00 only.
If your email is urgent please contact me directly on xxxx xxx xxxx.
Please note, non-urgent issues received by telephone will be deferred until the designated email response times.
Troubleshooting information on systems and applications is available on the wiki available at (insert link) and first line support is available from the service team on xxxx xxx xxxx or the self service portal at (insert link).
It's worth pointing out that we have next to no client contact, however the auto respond can be easily modified to apply to internal email addresses only therefore allowing external email's to be received as normal.
If you can get management on-side this approach can be effective, we saw a huge increase in telephone calls for the first couple of weeks but by sticking to the criteria you've set on what is urgent and what is appropriate to you within your remit, deferring the non-urgent correspondence to a set time and educating people on the appropriate resources to self-resolve issues has resulted in a massive drop in the correspondence we receive.
We backed up the trial with some metrics showing improved sprint outputs, decreased bugs etc. and now it's a permanent feature for our team.