Entanglement entropy and Page curve from the M-theory dual of thermal QCD above <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> at intermediate coupling

Exploration of entanglement entropy (EE) and obtaining the Page curve in context eternal black holes associated with top-down nonconformal holographic thermal duals at intermediate coupling has been entirely unexplored literature. We fill this gap by an neutral hole from a doubly setup relevant to M-theory dual QCD-like theories high temperatures (i.e., above ${T}_{c}$) (effected inclusion terms quartic curvature M theory). Remarkably, excluding higher derivative terms, EE Hawking radiation on-shell Wald integral (for appropriate choices constants integration appearing embeddings) increases almost linearly due dominance contribution Hartman-Maldacena (HM)-like surface ${S}_{\mathrm{EE}}^{\mathrm{HM},{\ensuremath{\beta}}^{0}},\ensuremath{\beta}\ensuremath{\sim}{l}_{p}^{6}$. This imparts ``Swiss-cheese'' structure ${S}_{\mathrm{EE}}^{\mathrm{HM},{\ensuremath{\beta}}^{0}}$ effecting ``Large N scenario'' (LNS). Then after time, island (IS) ${S}_{\mathrm{EE}}^{\mathrm{IS},{\ensuremath{\beta}}^{0}}$ dominates saturates linear time growth leads curve. The same is also obtained via areas Hartman-Maldacena-like/island surfaces. Requiring (${S}_{\mathrm{EE}}^{\mathrm{IS},{\ensuremath{\beta}}^{0}}$) per unit Hawking-Beckenstein (${S}_{\mathrm{BH}}$) post be around 2, positivity set respectively lower upper bound on horizon radius ${r}_{h}$ (the nonextremality parameter). Further, $\mathcal{O}({R}^{4})$ theory, fact turning point HM-like deep IR, requires relationship between ${l}_{p}$ along conjectural $\ensuremath{\gamma}\ensuremath{\equiv}{e}^{\ensuremath{-}\mathcal{O}(1){N}^{1/3}}$-suppression (motivated aforementioned requirement $\frac{{S}_{\mathrm{EE}}^{\mathrm{IS},{\ensuremath{\beta}}^{0}}}{{S}_{\mathrm{BH}}}\ensuremath{\sim}2$ up leading order). obtain hierarchy respect $\ensuremath{\gamma}$ ${S}_{\mathrm{EE}}^{\mathrm{HM},{\ensuremath{\beta}}^{0}},{S}_{\mathrm{EE}}^{\mathrm{IS},{\ensuremath{\beta}}^{0}}$ ${S}_{\mathrm{EE}}^{\mathrm{HM},\ensuremath{\beta}},{S}_{\mathrm{EE}}^{\mathrm{HM},\ensuremath{\beta}}$ [at $\mathcal{O}(\ensuremath{\beta})$]. existence massless graviton corresponding null mass eigenvalue Laplace-Beltrami equation internal space.