Energy evolution in many-particle quantum hydrodynamics of spinning plasmas

In this paper, we develop a quantum hydrodynamics (QHD) method for the research of the quantum evolution of a system of spinning particles. We derived the fundamental equation for charged and neutral spinning particles - the energy evolution equation from the many-particle microscopic Schredinger equation with a Spin-spin and Coulomb modified Hamiltonian. We derive the spin contributions to the energy evolution equation, thermal energy and thermal energy current.