Constant Temperature from Phase Space View of Ensembles of Excited States

Several decades ago Ghosh,Berkowitz and Parr^1 rewrote the ground-state density functional theory(DFT)into a local thermodynamics.They obtained a phase–space

Several decades ago Ghosh, Berkowitz and Parr 1 rewrote the ground-state density functional theory （DFT） into a local thermodynamics. They obtained a phase-space distribution function by maximizing the phase-space Shannon information entropy with fixed density and local kinetic energy density （of the DFT）. A local Maxwell-Boltzmann distribution function was resulted. They introduced the concept of local temperature. Though, there is only an analogy between the thermodynamics and the density functional theory of a single atom or molecule, it is still amazing that these systems can be considered as an ＂ideal gas＂. Even the fundamental equations 2 can be derived and the time-dependent density functional theory can be formalized as a thermodynamics with balance equations 3 for the energy and entropy.