  We study through the time evolution of magnetization the low temperature (T)
dynamics of the metastable coexisting phases created by traversing different
paths in magnetic field (H) and T space in a shape memory alloy system,
Ni$_{45}$Co$_{5}$Mn$_{38}$Sn$_{12}$. It is shown that these coexisting phases
consisting of a fraction of kinetically arrested austenite phase and remaining
fraction of low-T equilibrium martensitic phase undergo a slow relaxation to
low magnetization (martensitic) state but with very different thermomagnetic
history-dependent rates at the same T and H. We discovered that, when the
nucleation of martensitic phase is initiated at much lower T through the
de-arrest of the glass like arrested state contrasted with the respective first
order transformation (through supercooling at much higher T), then the long
time relaxation rate scales with the non-equilibrium phase fraction but has a
very weak dependence on T. This is explained on the basis of the H-T path
dependent size of the critical radii of the nuclei and the subsequent growth of
the equilibrium phase through the motion of the interface.
