What activities, be they physical or mental, do you use to improve your chess? Have you recently taken up something and noticed a positive change in your game? One thing I can think of is exercising such as walking or swimming. Are there any others?
I don't know of any correlations to physical exercise and chess skill, so I can't speak to walking or swimming.
What will probably give you the best return on your time would be memory enhancement exercises. These come in every style so I would just experiment and see what helps you. Any improvement on how much you can hold in your head will directly improve your chess game.
I also especially enjoy problems where you need to evaluate a board and determine the best move. I try to put time limits on myself to practice how quickly I can analyze a board without missing anything important.
There's probably no better way to improve chess than to study chess. I did seem to make an improvement by getting obsessed with Shogi, however. But this is a close relative of chess.
Actually, I would recommend a more physical hobby (rugby, rodeo clown, being a double-naught spy) to give yourself a break from the game. If you don't get burned out, you'll probably enjoy the game more and improve naturally.
May I suggest meditation? In my experience it improves concentration. One or two daily meditation sessions of 15 - 20 minutes each increases my ability to focus on tasks.
Unfortunately, I have no personal experience to relate to chess playing at this time, as my chess playing is currently suspended, other than an occasional low level game against the computer.
While not directly chess related, the relationship between exercise and cognitive abilities has been pretty intensely studied since the early 1900's. It has been shown through numerous studies that exercise does increase cognitive ability both during and after exercise. Oddly enough, it's also been shown that shorter and more intense physical exertion has a greater effect than endurance type training, at least in short term.
Most of the studies are looking at immediate effect, i.e. the cognitive task is usually done within minutes of finishing the exercise. Long term effects of exercise have gotten mixed results, however there are numerous meta-studies (more anecdotal in orientation than scientific) have reported many mental benefits to exercise.
One thing to note, is that exercise has definitively been proven to both help delay onset and mitigate symptoms of aging, such as cognitive impairment and dementia.
So, while exercise may not have a provable effect directly relating to OTB play, I highly recommend it.
One other thing to think about with this, even outside of physical fitness, is nutrition. Your brain soaks up a vast amount of glycogen to keep functioning even when "idling". If you are concentrating for a few hours on a game, you are going to be using even more, so for extended matches you should be thinking about some sort of food to help replace it, and the better your nutrition, the better prepared you will be in that respect as well.
For those interested in reading some of the research/studies, go to google scholar and use a search term such as "effects exercise cognitive performance" or similar.
The person recommending Go has a good idea, I believe. Go is more in-depth than chess, with a lot more abstract ideologies on how to attack, defend, and control space.
Physical activity keeps your mind healthy and fresh, so I recommend staying fit. I don't know any specific professionals that do this but I have heard before that professional players work out to stay on top of their game. Being physically healthy goes a long way to keeping your mind sharp, also in the mental endurance compartment. Cardio exercises matter more than strength, I suppose.
Also it helps to do EASY problems. These keep you honest and focused, instead of always doing challenging, convoluted problem-solving. Not to mention it helps keep your confidence high.
It may be what you need to cut out as much as what you need to add. I got a big jump in my play (and in other mental activities) once I stopped watching TV. There was quite simply less stuff to distract me and have me worry about. It sounds simple, but if your mind is cluttered by silliness and trivia and ads, there's more risk you can't focus on the game. I suppose this can apply to watching the Internet, too, if there are any websites that suck your time and energy away. I've seen studies saying that just spacing out is more restful than going down an Internet clickhole.
And it might be important to specify when as well as what. I like to exercise to take time out when thinking of a tough problem, so I think the study chess/exercise/see what you missed pattern can work very well. Taking breaks is important to learn anything. I'm not sure what sort of break is best for you, but make sure it's a real one. Also, I like to look at an important problem first thing in the morning so it's on my radar, whether it be for chess or programming or writing.
I also found that reading and studying literature really tore me away from chess to the point I found something new. I had all sorts of books I always meant to read. So that is a risk--you may find something even more fun than chess, for you, and it's tough to do two mentally tricky things at a high level.