Mini-meditation. Fold your hands in front of your keyboard and take two deep breaths. I do this every time I kick off a couple integration tests that hit the database. It keeps me from checking email while the tests execute and is relaxing.

Remind yourself of the task you are completing, then return to the task in 10 seconds.

10 seconds is enough time to get distracted, and spend 30 minutes checking email then browsing the internet (e.g., me writing this answer right now). Returning to the task at hand in 10 seconds is a powerful and productive thing you can do, surely moreso than many things that could take those 10 seconds. I strongly caution that any "productive" thing you can do given the 10 seconds you have will be far less productive than successfully returning to the task at hand in 10 seconds.

Think.

Ask yourself what are you doing next? How will you accomplish it?

Take a slow, deep breath, then exhale.

This should take around 5, maybe 10 seconds, and help you focus on the task at hand when the breath is done. It will not take much mental effort to take a breath.

Be bored.

Do not optimize those last 10 seconds away. It's like not pressing the accelerator when changing gears.

While ergonomic exercises and meditation are great ideas for recurring time slots, they usually require more than 10 seconds to have impact. I suggest to use 10secs for even easier tiny acts or thoughts, for which this timeframe will be enough to add value.

My tiny brain hacks:

1. Answer the question “What is the most important thing that I should do right now?”. The most common productivity mistake people do during the day is forgetting where they are with their plans and what is the most important thing for the moment. Taking 10 secs to sort this out several times during the day is gold. It creates a habit to always do the most important thing.
2. Create a new good habit or kill a bad one. The idea is to use a small punishment or reward to create a habit to think about something the way you need (or not think). For instance, put a rubberband around your wrist, and when you have 10 secs, analyze your thoughts, and if they are negative, snap the band as tough as possible to link them to pain. This will train your mind to instinctively avoid negative thinking. Or do the same trick if you find that at this moment you are not doing what you planned or not the most important thing (combining this technique with the above mentioned one).
3. Capture the most important idea from what you’ve just read or done. This habit is pure gold. Take 10 secs to write down 1-3 most important takeaways. This way you can train yourself to always see and remember the most important bits in anything you’ve just read, heard, saw or done.
4. Make a snapshot of your current state for further analysis. Many applications here: from physical parameters to mind state. You can capture: time + physical parameters using special gadgets, thought flow, your opinion on smth. important (like ask yourself: am I happy at this moment? If not - why? What I need to change right now to fix it?). Then analyze gathered snapshots when you have more time (say, on the weekend) to drive conclusions (why you are happy/not happy, what you need to change to achieve some goal, when you become less productive, etc.)

5. Generate ideas or solutions to problems. If you have a creative job where you need to generate ideas or just need some ideas / solutions, use 10 secs to come up with 1 idea/solution and put it down. Boom! By the end of the day/week you’ll have a huge list of them to pick up the best ones.

6. Set your Pomodoro timer for your next task. For those using the timer: in 10 secs you can decide what should be your next timed task, what time slot to allocate for it and set timer.

7. Visualize the next step you need to do. It helps to bring thoughts in order, tune into the matter and get prepared for action. If you pick up this technique for recurring 10sec slots, you will soon learn to visualize your goals very fast and clear, which is an invaluable skill to focus on anything at the speed of light (awesome for meetings, timed tasks, executing in stressful situations, fast decision making).
8. Repeat positive affirmations 1-3 times (mentally). For those who want to quickly calm down, initiate positive thinking, block fear, regain confidence, tune in the desired fashion. Just like Angela from Mr. Robot =)

Hope this helps

Unless you are already perfectly fresh it can be a decent opportunity to get some rejuvenation through a quick rest.

Meditation as said in another answer can be one way to do it, but you might also just close your eyes and take a supersonic nap.

10 seconds are very little but they are enough to be of some help, in many cases.

Such a brief time has the advantage that even if your company does not allow naps (a common circumstance, sadly):

• in 10 seconds it's not very likely that someone sees you
• if someone sees you it's entire plausible that you just took some seconds to think with your eyes closed
• you can feel right with your conscience, because there's no way you could have dome something significantly more productive in 10 seconds
• even the sternest company is likely to not make a fuss for a nap of 10 seconds

You're strongly advised to set a timer before, it's entirely possible to fall right asleep and that should actually be your aim; you just want to wake up in 10 seconds, not 2 hours or when your boss shakes you up.

I think humans are different from machines and you should not consider yourself a machines. In your scenario, what you can do in 10 seconds is read some stuff on new tab.