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In general, different bipartition choices do not lead to the same results for the generalizations to finite temperatures χF (g,β ) or d s2 (g,β ). Indeed, while the "quantum" parts in Eqs. are identical (up to a factor of g2) whether we consider H0 or g H1 as the "driving term," this is not the case for the "classical" contribution [Eq. ], indicating that there is no simple relationship between χF H0 (β) and χF g H1 (β) at finite β. However, at low enough temperature, the classical contribution becomes negligible and we recover χF H0 (β→∞ ) = g2 χF g H1 (β→∞ ), as shown in Fig. f3.
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In general, different bipartition choices do not lead to the same results for the generalizations to finite temperatures χ F (g, β) or d s 2 (g, β). Indeed, while the "quantum" parts in Eqs. are identical (up to a factor of g 2) whether we consider H 0 or g H 1 as the "driving term," this is not the case for the "classical" contribution [Eq.], indicating that there is no simple relationship between χ F H 0 (β) and χ F g H 1 (β) at finite β. However, at low enough temperature, the classical contribution becomes negligible and we recover χ F H 0 (β → ∞) = g 2 χ F g H 1 (β → ∞), as shown in Fig.f3.
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