Fig. 3: Entropy changes as a function of dimension.
From: Mixing indistinguishable systems leads to a quantum Gibbs paradox
Series of plots showing ΔSinfo, ΔSigno against the total cell number d of the system. a, b Bosonic systems of particle number n = 4 and n = 24 respectively. c, d The same for fermionic systems. Note that we have taken the initial number of particles on either side of the box to be equal, n = m in all cases. For comparison, all four figures also display the classical changes in entropy for an informed/ignorant observer. The behaviour of the deficit between ΔS for an informed/ignorant observer of quantum particles agrees with the low density limit in Eq. (23) where we can see ΔSinfo tending to the classical limit \(2n\,\mathrm{ln}\,(2)\) with ΔSigno trailing behind by a deficit of n2/2d2 + H(p). Additionally, by comparing the different plots, we can see the low-dimensional fermionic advantage where the change in entropy is even greater than the classical \(2n\,\mathrm{ln}\,(2)\) value.
