Aircraft propulsion system with power turbine electric machine

An aircraft system is provided that includes an open propulsor rotor, a turbine engine and a power turbine electric machine. The turbine engine includes a core compressor section, a core combustor section, a core turbine section, a power turbine section, a flowpath, a first core rotating structure and a power turbine rotating structure. The first core rotating structure includes a first core compressor rotor and a first core turbine rotor. The first core compressor rotor is disposed in the core compressor section. The first core turbine rotor is disposed in the core turbine section. The power turbine rotating structure is configured to drive rotation of the open propulsor rotor. The power turbine rotating structure includes a power turbine rotor disposed in the power turbine section. The power turbine electric machine is operatively coupled to the power turbine rotating structure.