  A closed system of the equations for the local Bloch vectors and spin
correlation functions is obtained by decomplexification of the Liouville-von
Neumann equation for 4 magnetic particles with the exchange interaction that
takes place in an arbitrary time-dependent external magnetic field. The
analytical and numerical analysis of the quantum thermodynamic variables is
carried out depending on separable mixed initial state and the magnetic field
modulation. Under unitary evolution, non-equilibrium reversible dynamics of
power production in the finite environment is investigated.
