Fundamental formalism of statistical mechanics and thermodynamics of negative kinetic energy systems

Abstract

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.

12 pages, 2 tables

References in corpus (4)

• Equilibration rates and negative absolute temperatures for ultracold atoms in optical lattices
• Atomic Gases at Negative Kinetic Temperature
• Solving Klein's paradox
• New results by low momentum approximation from relativistic quantum mechanics equations and suggestion of experiments

Cited by in corpus (4)

• The modified fundamental equations of quantum mechanics
• There is no vacuum zero-point energy in our universe for massive particles within the scope of relativistic quantum mechanics
• A generalized scattering theory in quantum mechanics
• A physical mechanism of the generation of stable positive kinetic energy systems and a qualitative explanation of the proportions of the four ingredients in the universe