Table 2 Summary of results.
From: Mixing indistinguishable systems leads to a quantum Gibbs paradox
Quantum | Classical | Quantum | Quantum | Classical | |
|---|---|---|---|---|---|
Limit | (no limit) | (no limit) | (d ≫ n) | (d ≫ n ≫ 1) | (d ≫ n ≫ 1) |
ΔSinfo | \(2{\mathrm{ln}}\,\left(\begin{array}{c}n\,+\,d\,-\,1\\ n\end{array}\right)\,\\ -\,2{\mathrm{ln}}\,\left(\begin{array}{c}n\,+\,d/2\,-\,1\\ n\end{array}\right)\) | \(2{\mathrm{ln}}\,\left(\begin{array}{c}n\,+\,d\,-\,1\\ n\end{array}\right)\,\\ -\,2{\mathrm{ln}}\,\left(\begin{array}{c}n\,+\,d/2\,-\,1\\ n\end{array}\right)\) | … | \(\approx\!2n\,{\mathrm{ln}}\,2\) | \(\approx \!2n\,{\mathrm{ln}}\,2\) |
ΔSigno | \({\sum }_{J}{p}_{J}{\mathrm{ln}}\,{d}_{J}^{B}\,\\ -\,2{\mathrm{ln}}\,\left(\begin{array}{c}n\,+\,d/2\,-\,1\\ n\end{array}\right)\) | \({\mathrm{ln}}\,\left(\begin{array}{c}2n\,+\,d\,-\,1\\ 2n\end{array}\right)\,\\ -\,2{\mathrm{ln}}\,\left(\begin{array}{c}n\,+\,d/2\,-\,1\\ n\end{array}\right)\) | \(\approx\!{{\Delta }}{S}_{\text{info}}\,-\,H({\bf{p}})\) | \(\approx\!2n\,{\mathrm{ln}}\,2\) | ≈ 0 |
