Influence of thermal noise on the field-driven dynamics of the non-collinear antiferromagnet Mn3Sn

$\mathrm{Mn_3Sn}(0\overline{1}\overline{1}0)[0001]$ experiences a tensile strain when grown epitaxially on $\mathrm{MgO}(110)[001]$, and thus the energy landscape changes from six-fold symmetry to two-fold symmetry. External magnetic field further breaks the symmetry and the \textcolor{black}{resulting energy landscape is sensitive to} the field orientation relative to the easy axis. \textcolor{black}{In the presence of thermal noise,} the relaxation of the magnetic octupole moment in \textcolor{black}{a strained Mn$_3$Sn film} is composed of four distinct escape processes involving the two saddle points and two equilibrium states in the energy landscape. Here, we apply harmonic transition-state theory to derive analytical expressions for the inter-well escape time and octupole moment relaxation time, both influenced by an external symmetry-breaking magnetic field and finite thermal noise in the intermediate-to-high damping regime. The analytical predictions are in strong agreement with comprehensive numerical simulations based on coupled LLG equations. The results presented here are crucial toward realizing Mn$_3$Sn's applications in random number generation and probabilistic computing.