The solutions of a particle’s Dirac equation contains a negative kinetic energy (NKE) branch. Such an energy spectrum has an upper limit but no lower limit, so that the system with this spectrum, called NKE system, is of negative temperature. Fundamental formulas of statistical mechanics and thermodynamics of NKE systems are presented. All the formulas have the same forms of those of positive kinetic energy (PKE) systems. Almost all thermodynamic quantities, except entropy and specific heat, have a contrary sign compared to those of PKE systems. Specially, pressure is negative and its microscopic mechanism is given. Entropy is always positive and Boltzmann entropy formula remains valid. The three laws of thermodynamics remain valid, as long as the thermodynamic quantities have a negative sign. Negative temperature Carnot engine can work between two negative temperatures. Since the NKE levels need not be fully filled, it is argued that the concept of Dirac’s Fermion Sea can be totally abandoned.

粒子狄拉克方程的解包含负动能 (NKE) 分支。这样的能谱有上限但没有下限，因此具有该能谱的系统称为NKE系统，温度为负。介绍了 NKE 系统的统计力学和热力学的基本公式。所有公式都具有与正动能 (PKE) 系统相同的形式。与 PKE 系统相比，几乎所有的热力学量，除了熵和比热，都具有相反的符号。特别地，压力是负的，并给出了它的微观机制。熵始终为正，玻尔兹曼熵公式仍然有效。只要热力学量具有负号，热力学三定律仍然有效。负温度卡诺发动机可以在两个负温度之间工作。由于 NKE 水平不需要完全填充，有人认为可以完全放弃狄拉克费米子海的概念。