  Irreversible processes are frequently adopted to account for the entropy
increase in classical thermodynamics. However, the corresponding physical
origins are not always clear, e.g. in a free expansion process, a typical model
in textbooks. In this letter, we study the entropy change during free expansion
for a particle with the thermal de Broglie wavelength ($\lambda_{T}$) in a
one-dimensional square trap with size $L$. By solely including quantum
dephasing as an irreversible process, we recover classical result of entropy
increase in the classical region ($L\gg\lambda_{T}$), while predict prominent
discrepancies in the quantum region ($L\ll\lambda_{T}$) because of
non-equilibrium feature of trapped atoms after expansion. It is interesting to
notice that the dephasing, though absent in classical system, is critical to
clarify mysteries in classical thermodynamics.
