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.

There is no vacuum zero-point energy in our universe for massive particles within the scope of relativistic quantum mechanics

“…21 and 22. The statistical mechanics and thermodynamics of the NKE systems were elaborated 21 and related macroscopic mechanics was given. 23 As soon as the status of the NKE was promoted to the same as that of the PKE, the field of QM was extended to the domain of the NKE, and a series work needed to be done.…”

“…The points 2, 4, 6, 7 and 9 were dealt with in Refs. [20,21,23]. The present paper intends to deal with point 1.…”

“…The reflection coefficient of one-dimensional step potential was recalculated, 22 and this treatment was in line with that for relativistic particles. 21 The example in Ref. 22 was a simple one since the potential was piecewise constants.…”

“…In Section II, the harmonic oscillator model in QM is discussed, and the the conclusion is that there is no ZPE so that the inconsistence between cases (4) and ( 5) in TABLE I is removed. As for the inconsistence between cases (1)-( 3), it concerns second quantization, and will be treated in a later work which will be based on the investigation in [19][20][21][22][23][24][25]. Section III will discuss the vacuum zero-point energy (VZPE) of our universe, which is the origination of the problem of cosmological constant.…”

Evaluation of cross section of elastic scattering for non-relativistic and relativistic particles by means of fundamental scattering formulas

“…Hence, all the field concerning the PKE ought to be studied in the aspect of the NKE. Based on this premise, a series work has been done [1][2][3][4][5][6][7]. Up to now, the research is within the scope of relativistic quantum mechanics (RQM).…”