Non-equilibrium open systems and non-equilibrium thermo field dynamics

Within the formalism of non-equilibrium thermo field dynamics (NETFD), a derivation of basic equations is given in their most general and suitable forms to take into account the coarse graining in the kinetic region and in the fluid mechanical region. A new concept, called the connection of thermal spaces, is introduced in order to give a prospect to overcome the problem of the specification of representation spaces in far-from-thernal equilibrium situations where systems traverse unitarily inequivalent representation spaces in their dynamical evolutions.