Existence of A Rigorous Density-Functional Theory for Open Electronic   Systems
  We prove that the electron density function of a real physical system can be uniquely determined by its values on any finite subsystem. This establishes the existence of a rigorous density-functional theory for any open electronic system. By introducing a new density functional for dissipative interactions between the reduced system and its environment, we subsequently develop a time-dependent density-functional theory which depends in principle only on the electron density of the reduced system. 
Xiao Zheng, Fan Wang, and GuanHua Chen