Search the web for "staying productive over the holidays" spills out dozens of supposedly helpful articles but with all due respect, such articles are woefully misguided. The holiday work slump isn't a problem--it's a productivity boost. Here's why.
During the holidays the mood inside most workplaces gets lighter. There are more social chit-chats, more impromptu snack breaks, and just as important, fewer official meetings. This gives everyone a chance get to strengthen relationships with their coworkers.
This is, of course, the supposed purpose behind the infamous holiday party. Such parties, however, tend to be either stilted and uncomfortable or, worse, occasions for embarrassing drunken misbehavior. Holiday parties, if anything, weaken coworker relationships.
When you just sort of "hang out" with people at work, without all that much to do, you've got the time to get to know people, especially those outside your immediate group. You've got a chance to make friends, which increases group cohesiveness and collaboration.
By contrast, if you push to make the holiday season into just more of the same-old-same-old, you're missing the opportunity to naturally and easily turn the workplace from a collection of individuals into an actual community, which ultimately increases productivity.
But that's not all.
Today's dominant corporate culture, especially in the United States, is "penny-wise and pound-foolish" when it comes to work hours and vacations. While long work hours and missed vacation days seem like productivity boosts, they're actually the opposite.
There is significant evidence is that consistently working long hours (i.e. beyond 40 hours a week) decreases rather than increases productivity. Similarly, skipping vacation adds to employee burnout and creates health problems, like heart disease.
Employees who burnout or become overstress and sick tend to leave a company to work elsewhere. This means a loss of expertise, and as well as additional (and often quite substantial costs) to recruit, train, and on-board replacements.
In an ideal world, companies would go give employees a more reasonable work schedule and encourage rather than discourage them from taking their paid vacation. But we're not in an ideal world, so neither of those things are going to happen any time soon.
And it's not just management that's at fault here.
In many companies, coworkers compete with each other, consciously or unconsciously, to see who can work longer hours. (Winner gets humblebraggring rights.) Similarly, coworkers often "vacation shame" employees who actually take their paid days off.
The holiday slump is the last remaining "perk" where it's socially acceptable for everyone to relax and let their batteries recharge. That way everyone hits the ground running in the new year, both refreshed and newly committed to everyone's mutual success.