A nonequilibrium statistical operator (NSO) is built for classical sistems using a field theory in classical phase space, which is but a classical version of the thermofield dynamics formalism. The approach developed here starts with a second-quantized version of this phase-space field theory. Then elements of symmetry are analysed and invariants of the theory are introduced. The local conservation laws are derived and used to make explicit NSO. Such a method is applied to derive the Fokker-Planck-Kramers equation.