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 ($Lgglambda_{T}$), while predict prominent discrepancies in the quantum region ($Llllambda_{T}$) 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.
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