arXiv subjects
Publications and source records attributed to Q. A. Wang.
In this paper, we show that 1) additive energy is not appropriate for discussing the validity of Tsallis or Rényi statistics for nonextensive systems at meta-equilibrium; 2) $N$-body systems with nonadditive energy or entropy should be described by generalized statistics whose nature is prescribed by the existence of thermodynamic stationarity. 3) the equivalence of Tsallis and Rényi entropies is in general not true.
Recently, Gross claims that Boltzmann entropy $S=k\ln W$ is valid for any system at equilibrium, so that Tsallis entropy is useless in this case. I comment on some arguments forwarded to reach this conclusion and argue that the additive energy formalism of nonextensive statistics is not appropriate for the fundamental study of the theory for nonadditive systems.
The pressure influence on the lattice vibration of $CaZnF_4$ has been studied by Raman diffusion up to 17 GPa. Most Raman frequencies increase with increasing pressure. Three singularities in the pressure induced frequency evolution are observed around 1.5 GPa, 10 GPa and 17 GPa. The samples pressurized to 17 GPa or higher do not revert to the ambient pressure phase after being released, the new phase showing different Raman spectra from the ordinary one. It is suggested that $CaZnF_4$ undergoes probably sudden lattice deformations at about 1.5 GPa and 10 GPa, and an irreversible phase transformation above 17 GPa.
The pressure effect on the fluoride scheelite laser host $LiYF_4$ is studied at room temperature up to 26 GPa by Raman scattering and up to 40 GPa by $P^{3+}$ fluorescence of doped sample. The Raman spectra exhibit three singularities at the vicinity of 6 GPa, 10-12 GPa and 16-17 GPa. The samples pressurized to 21 GPa or higher do not recover the original phase after being released, giving more Raman lines than original samples. The luminescence spectra of $P^{3+}$ are collected in the energy range corresponding to following transitions $^3P_{0,1}--^3H_{4,5,6}$, $^1D_2--^3H_4$ and $^3P_0--^3F_2$. Singularities are observed in the vicinity of 6 GPa, 10 GPa, 16 GPa, 23 GPa in agreement with the Raman study. Moreover, an irreversible transition occurs at 23 GPa. The samples pressurized to above 26 GPa become amorphous when released and all the sharp lines disappear. Above 31 GPa, the spectra at high pressures show only some broad bands corresponding to transitions between two multiplets of the $^4F_2$ configuration of $Pr^{3+}$. These singularities suggest possible phase transformations leading to lowering of the lattice symmetry.
We comment on the problem of energy translation invariance of probability distribution and present some observations. It is shown that a probability distribution can be invariant in the thermodynamic limit if there is no long term interaction or correlation and no relativistic effect. So this invariance should not be considered as a universal theoretical property. Some peculiarities within the invariant $q$-exponential distribution reveal that the connection of the current nonextensive statistical mechanics to thermodynamics might be disturbed by this invariance.
The problem of factorization of a nonextensive probability distribution is discussed. It is shown that, in general, the correlation energy between the correlated subsystems in the canonical composite system can not be neglected even in the thermodynamic limit. In consequence, the factorization approximation should be employed carefully according to different systems. It is also shown that the zeroth law of thermodynamics can be established in the framework of the Incomplete Statistical Mechanics (ISM).