Energy minimization conjecture for the directed volume of K-plus

Let $V$ be a vector space and let $K\subset V$ be a centrally symmetric convex body. Define

$$K^+=\{(\vec{x},\vec{y})\in K\times K^\circ\mid\langle\vec{x},\vec{y}\rangle=1\}.$$

Let $\operatorname{\stackrel{\longrightarrow}{Vol}}K^+$ denote its directed volume, and let $Q(\operatorname{\stackrel{\longrightarrow}{Vol}}K^+)$ be the energy of that directed volume.

Energy conjecture. The quantity $Q(\operatorname{\stackrel{\longrightarrow}{Vol}}K^+)$ is uniquely minimized when $K$ is an ellipsoid.

The source presents this conjecture as one that implies the bottleneck conjecture and may be equivalent to it. No resolution is reported.