Thermodynamical transcription of the density functional theory with constant temperature. Issue 16 (24th April 2017) - Nagy, Ágnes
Abstract: The thermodynamical interpretation of the density functional theory for an electronic ground state is revisited. Ghosh et al. invented the thermodynamical transcription of the ground‐state density functional theory into a local thermodynamics. They introduced the idea of the local temperature that varies from point to point. The local temperature is defined via the kinetic energy density. The kinetic energy density is not uniquely defined, usually the everywhere positive gradient form is applied. Now we prove that it is possible selecting the kinetic energy density so that the local temperature be a constant for the whole system under consideration. The kinetic energy density is proportional to the electron density and the temperature is proportional to the kinetic energy. Furthermore, the kinetic energy density corresponding to the constant temperature, maximizes the information entropy. Abstract : The kinetic energy density is not uniquely defined. It is proved that the extremum information entropy principle leads to a kinetic energy density proportion to the electron density. Then, the local temperature is a constant for the whole system under consideration.