How isolated is enough for an "isolated" system in statistical mechanics?

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.