Ghosh, Berkowitz and Parr designed a thermodynamical transcription of the ground-state density functional theory and introduced a local temperature that varies from point to point. The theory, however, is not unique because the kinetic energy density is not uniquely defined. Here we derive the expression of the phase–space Fisher information in the GBP theory taking the inverse temperature as the Fisher parameter. It is proved that this Fisher information takes its minimum for the case of constant temperature. This result is consistent with the recently proven theorem that the phase–space Shannon information entropy attains its maximum at constant temperature.

Ghosh，Berkowitz和Parr设计了基态密度泛函理论的热力学转录，并介绍了随点变化的局部温度。但是，该理论不是唯一的，因为动能密度不是唯一定义的。在这里，我们以反温度为Fisher参数，推导了GBP理论中相空间Fisher信息的表达式。事实证明，对于恒定温度，该Fisher信息将其最小值降至最低。这一结果与最近证明的定理一致：相空间香农信息熵在恒定温度下达到最大值。