I have read in this book, simulated annealing, on page 40-41, if temperature $t$ tend to $0$, then the stationary distribution will be distributed among optimal solutions. What i can not understand here is that, if with temperature $0$, the stationary distribution will be distributed among optimal solutions, so why we need to have initially large temperature and reduce it slowly, so that at each temperature, the algorithm reaches the thermal equilibrium? Why do not we set the temperature to $0$ at the start of the algorithm and iterating until reaching thermal equilibrium for temperature $0$.
Form physical point of view, i know that, if in the annealing process, the temperature reduced quickly, the meta-stable amorphous structures will be reached rather than the low energy crystalline lattice structure. But from theoretical point of view, i can not understand the depth of the subject.