On the semi-additivity of the $1\mathrm{/}2$-symmetric caloric capacity

In this paper we study properties of a variant of the $1\mathrm{/}2$-caloric capacity, called $1\mathrm{/}2$-symmetric caloric capacity. The latter is associated simultaneously with the $1\mathrm{/}2$-fractional heat equation and its conjugate. We establish its semi-additivity in ${\mathbb{R}}^{n+1}$ and, moreover, we compute explicitly the $1\mathrm{/}2$-symmetric caloric capacity of rectangles, which illustrates its anisotropic behavior.