Hmm, not really physics per se.. But I could imagine a game based on numerical methods (I do too many calculations) :)
Player 1 has a piece on a board, and gets to move to a number of spots, 'degrees of freedom'. Player 2 has to guess which spot P1 is going to move to. If P2 correctly anticipates which move P1 makes, then P1 loses a degree of freedom for his next move. If P2 did not correctly guess, then P1 gains a degree of freedom.
P2's goal is to get P1 to converge, by trapping him into a situation where he cannot move. P1's goal is to diverge, by getting some number of degrees of freedom that predicting his next move is deemed impossible. You'd have to come up with some interesting board design and specific rules to make sure the game was balanced.
Now that I think of it, there are already a number of games which (chess, go, hex) which indirectly include this concept to varying extents. But I suppose that just goes to show it's a fruitful idea.