Nice question. I thought about this for some time. Fortunately, I have a friend in physiology who is an expert in this business. He said that muscles under tension, or compression actually consume energy by metabolizing ATP, the chemical energy carrier in the body. In technical terms it's the difference between systolic and diastolic metabolism.
Although you are doing no work on the wall, you are still eating up ATP energy by keeping your muscles clenched. Eventually you get tired.
LeeH
p.s. I think that inside the muscle, there's a little slippage of the myosin-actin bonds. You have to do work to overcome that slippage, just as the engine of a car on a slope has to do work to keep it stationary if the tires are slipping a bit on the slope. Mike W.
(published on 10/01/2012)