  We quantify the probability per unit Euclidean-time of reversing the
magnetization of a $\pi$-Bloch vector, which describes the Ferromagnetic Domain
Walls of a Ferromagnetic Nanowire at finite-temperatures, by evaluating the
saddlepoint solution of the grand canonical partition function for the
Ferromagnetic Nanowire consisting of $N$ such soliton and anti-soliton states.
Our approach, based on Langer's Theory, treats the double Sine-Gordon model
that defines the $\pi$-Bloch vectors via a procedure of nonperturbative
renormalization, and uses importance sampling methods to minimise the free
energy of the system, and identify the saddlepoint solution corresponding to
the reversal probability. We identify that whilst the general solution for the
free energy minima cannot be expressed in closed form, we can obtain a closed
expression for the saddlepoint by maximizing the entanglement entropy of the
system. We use this approach to quantify the geometric and non-geometric
contributions to the entanglement entropy of the Ferromagnetic Nanowire,
defined between entangled Ferromagnetic Domain Walls, and evaluate the
Euclidean-time dependence of the domain wall width and angular momentum
transfer at the domain walls, which has been recently proposed as a mechanism
for Quantum Memory Storage.
