As someone who suffers from depression and anxiety, i have noticed how true the statement is when they say everything that you deal with mentally has a physical counterpart. I would notice especially with anxiety, that if i had to deal with a 0-60 crisis situation after it was over, i would be absolutely exhausted. I mean seriously! Totally worn out. I would usually have to take a nap after because I was physically beat as well as psychologically.
I noticed that i think the same is true the other way. When i am doing something really physical, it is hard for me to put 100% concentration into anything else specifically. It is all or nothing.
I have also found that when both collide and you have to be pushed to your physical limit and mental limit at the same time, meaning that while you are physically busting ass, you are also multitasking multiple highly stressful things in your head and trying to keep it all straight, (especially if you add very limited sleep to the equation) you are pushed to your limits. It is amazing because it shows us just what we can do but if you go full speed, overtime, with afterburners, something will eventually have to give (usually being your health). Just think of those days when you were shuffling 3 jobs AND full semesters in college or working and having a new born baby while keeping the house clean and fixing dinner all by yourself.
It pushes us to the limits. It is probably better actually to have a good workout in both physical and mental fronts regularly. I guess i could just say, that THIS is where I personally have trouble multi-tasking. The depression does not help at all (making everything that much more dire which adds stress to the already stressed situation), but i find that for me personally, my anxiety is an action reaction, depression gives me sedative results. It is difficult to feel both insomniac and super tired simultaneously. I can however cook dinner, read a book listen to music, do dishes and talk on the phone at the same time though. Just as long as i am not finding out that, say, my identity has been stolen and my bank account frozen!
*afterthought note* I think that when we have something on like tv or radio (or people talking/ screaming) all the time, we can mentally wither. We need several minutes of silence for our brains kinda like we need a few bites of food and a some rest for our bodies. If you stay at home watching tv all day AND feel exhausted, try turning off the tv and opening a book if you are bored. Your few minutes of quiet air may invigorate you almost as much as getting up and moving around. Imagine how good you would feel if you did both!!