Entropy production and equilibration in Yang-Mills Quantum Mechanics

We discuss a general and systematic method of obtaining the coarse grained entropy of a quantum system based on the Husimi distribution. In this method we construct a coarse grained Hamiltonian whose expectation value is exactly conserved. As an example, we solve numerically the equation of motion for the Husimi distribution for two-dimensional Yang-Mills quantum mechanics. Moreover, we evaluate the time evolution of the coarse grained entropy of a highly excited state, and show that the coarse grained entropy saturates to a value that coincides with the microcanonical entropy.