  We apply a new method based upon thermofield dynamics (TFD) to study
entanglement of finite-spin systems with non-competitive external fields for
both equilibrium and non-equilibrium cases. For the equilibrium finite-spin
systems, the temperature dependence of the extended density matrices is derived
using this method, and the effect of non-competitive external field is
demonstrated. For the non-equilibrium finite-spin systems, the time dependence
of the extended density matrices and the extended entanglement entropies is
derived in accordance with von Noumann equation, and the dissipative dynamics
of the finite-spin systems is argued. Consequently, the applicability of the
TFD-based method to describe entanglement is confirmed in both equilibrium and
non-equilibrium cases with the external fieds.
