The concepts of local temperature, local entropy, and local free energy density are introduced within the framework of the ground-state density-functional theory of many-electron systems, and a complete local thermodynamic picture is then developed. A view emerges of the electron cloud, as analogous to a classical inhomogeneous fluid moving under gradients of temperature, pressure, and an effective potential, described by a locally Maxwellian distribution.
Ghosh et al. (Sat,) studied this question.