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 (
λT) 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≫λT), while predict prominent discrepancies in the quantum region (
L≪λT) 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.
It was recently shown by Bartelmann et al. how correlated initial conditions can be introduced into the statistical field theory for classical particles pioneered by Das and Mazenko. In this paper we extend this development from the canonical to the grand canonical ensemble for a system satisfying statistical homogeneity and isotropy. We do this by translating the probability distribution for the initial phase space coordinates of the particles into an easy diagrammatic representation and then using a variant of the Mayer cluster expansion to sum over particle numbers. The grand canonical generating functional is then used in a structured approach to the derivation of the non-interacting cumulants of the two core collective fields, the density
ρ and the response field
B. As a side-product we find several theorems pertaining to these cumulants which will be useful when investigating the interacting regime of the theory in future work.