  As predicted by the second law of thermodynamics, the increase of entropy is
irreversible in time. However, in quantum mechanics the evolution of quantum
states is symmetrical about time-reversal, resulting a contradiction between
thermodynamic entropy and quantum entropy. We study the W entropy, which is
calculated from the probability distribution of the wave function on Wannier
basis, in hard-core boson system. We find that W entropy and F entropy, which
is calculated from the probability distribution of the wave function on Fock
basis, satisfy an approximately linear relationship and have the same trend.
Then, we investigate the evolution of W entropy for various parameters. We
calculate the regression period of W entropy and find its dependence on the
lattice scale. Our results show that the second law of thermodynamics is not
completely valid in quantum mechanics. The behaviour of W entropy obeys the
second law of thermodynamics, only when the system scale is large enough.
