I can not claim that I fully understand my own question, but I feel it is worth sharing. Suppose there is a physical system composed of MxN degree of freedom where M is the number of the states and N the number of particles. When a measurement is undertaken, the physical system collapses to well defined state that represents the eigen value of the physical observable. The result is an inevitable increase in the total entropy of the (system+the measuring machine+the universe) in the form of heat. What if MxN is the physical universe itself, where does the heat go?