This is what I call a transference of tension. It may or may not be directly related to piano playing (not knowing anything about you or your other activities), but I'd be willing to bet that there's at least a connection.
Have you ever noticed how bodybuilders' arms are permanently curled? Or how about this: have you ever had a friend hold your arms firmly while you tried to push them up, and then when he let go, your arms sort of "flew up" by themselves (when I was a kid, this was cool little trick we did sometimes). This is the result of muscles and ligaments getting used to a certain motion or exertion without compensation. Personal trainers will tell you that for every muscle group you work, you should work the opposite muscle group equally. For instance, if you work your abs, you should also work your back to equal things out.
With the piano, it's a little different, since there's not a lot you can do to work opposite muscle groups, but stretching definitely helps. If you want, I could describe some stretches that I think would help "loosen up" those arms and hands.
Lastly, try this: clench your hand as tight as you can, then stretch it out as far as you can. Then let your hands relax completely. The shape of your hand after you relax it is your natural hand shape, and this is the shape that will allow you optimum relaxation while playing.
Peace,
Bri