EDDINGTON'S “Internal Constitution of the Stars” was published in 1926 and gives what now ranks as a classical account of his own researches and of the general state of the theory at that time. Since then, a tremendous amount of work has appeared. Much of it has to do with the construction of stellar models with different equations of state applying in different zones. Other parts deal with the effects of varying chemical composition, with pulsation and tidal and rotational distortion of stars, and with the precise relations between the interior and the atmosphere of a star. The striking feature of all this work is that so much can be done without assuming any particular mechanism of stellar energy-generation. Only such very comprehensive assumptions are made about the distribution and behaviour of the energy sources that we may expect future knowledge of their mechanism to lead mainly to more detailed results within the framework of the existing general theory. An Introduction to the Study of Stellar Structure By S. Chandrasekhar. (Astrophysical Monographs sponsored by The Astrophysical Journal.) Pp. ix+509. (Chicago: University of Chicago Press; London: Cambridge University Press, 1939.) 50s. net.

An Introduction to the Study of Stellar Structure

Preface. 1. Plasmas and Dust. 2. Charging Mechanisms and Experiments. 3. Space Observations. 4. Multispecies Formalism and Waves. 5. Electrostatic Modes. 6. Electromagnetic Modes. 7. Fluctuating Dust Charges. 8. Self-Gravitation. 9. Mass and Size Distributions. 10. Other Modes. 11. Conclusions and Outlook. Bibliography. Index.

https://physicstoday.scitation.org/doi/pdf/10.1063/1.1404853

Waves in Dusty Space Plasmas

Tsallis holographic dark energy

Generalized entropy formalism and a new holographic dark energy model

We present measurements of galaxy clustering from the Baryon Oscillation Spectroscopic Survey (BOSS), which is part of the Sloan Digital Sky Survey III (SDSS-III). These use the Data Release 9 (DR9) CMASS sample, which contains 264 283 massive galaxies covering 3275 square degrees with an effective redshift z = 0.57 and redshift range 0.43 < z < 0.7. Assuming a concordance ΛCDM cosmological model, this sample covers an effective volume of 2.2 Gpc, and represents the largest sample of the Universe ever surveyed at this density, n̄ ≈ 3× 10−4h−3Mpc. We measure the angle-averaged galaxy correlation function and power spectrum, including density-field reconstruction of the baryon acoustic oscillation (BAO) feature. The acoustic features are detected at a significance of 5σ in both the correlation function and power spectrum. Combining with the SDSS-II Luminous Red Galaxy Sample, the detection significance increases to 6.7σ. Fitting for the position of the acoustic features measures the distance to z = 0.57 relative to the sound horizonDV /rs = 13.67±0.22 at z = 0.57. Assuming a fiducial sound horizon of 153.19 Mpc, which matches cosmic microwave background constraints, this corresponds to a distance DV (z = 0.57) = 2094 ± 34 Mpc. At 1.7 per cent, this is the most precise distance constraint ever obtained from a galaxy survey. We place this result alongside previous BAO measurements in a cosmological distance ladder and find excellent agreement with the current supernova measurements. We use these distance measurements to constrain various cosmological models, finding continuing support for a flat Universe with a cosmological constant.

SDSS-III Baryon Oscillation Spectroscopic Survey: baryon acoustic oscillations in the data Release 9 spectroscopic galaxy sample.

Blackbody radiation is reconsidered using the counterpart of the Bose-Einstein distribution in the $\ensuremath{\kappa}$ statistics arising from the Kaniadakis entropy. The generalized Planck radiation law is presented and compared to the usual law, to which it reduces in the limiting case $\ensuremath{\kappa}\ensuremath{\rightarrow}0$. Effective Einstein's coefficients of emission and absorption are defined in terms of the Kaniadakis parameter $\ensuremath{\kappa}$. It is shown that the Kaniadakis statistics keeps unchanged the first Einstein coefficient $A$ while the second coefficient $B$ admits a generalized form within the present theoretical framework.

Planck radiation law and Einstein coefficients reexamined in Kaniadakis κ statistics.

Quantum ion-acoustic solitary waves are studied by considering the effects of exchange and correlation for the electrons. Starting from one-dimensional quantum hydrodynamic equations, including the term of exchange correlation for electrons, we obtain a model in which two dimensionless parameters appear (in addition to the parameter measuring the quantum diffraction) measuring the exchange and the correlation. A new deformed Korteweg--de Vries equation is derived. The effect of exchange and correlation is reflected in the phase speed as well as in the nonlinear and dispersion terms. Its solution shows that the exchange-correlation effects modify the amplitude as well as the width of the weak solitary waves. In the arbitrary amplitude regime, and as may be expected, a pseudopotential analysis shows that the exchange-correlation effects may change the nature (compressive or rarefactive) of the quantum ion-acoustic solitary waves. Our results complement and give new insight into the previously published work on this problem.

Quantum ion-acoustic solitary waves: the effect of exchange correlation.

We propose to put the well-known nonthermal and suprathermal empirical distributions, used in plasma physics, onto a more rigorous foundation. Their use is frequently criticized because of a lack of formal derivation and physical explanation. A connection between these non-Maxwellian distributions and the Beck-Cohen superstatistics is suggested. They are perceived as a consequence of typical temperature fluctuations. We show that the suprathermal distribution is generated by the Γ distribution of the inverse temperature, in the same way as the Tsallis q statistics. The nonthermal distribution also follows from the χ(2) distribution, with a small variance. Our contribution provides a possible physical meaning for these ad hoc distributions.

Nonthermal and suprathermal distributions as a consequence of superstatistics.

A first use of Kaniadakis entropy in the context of quantum information is presented. First we show that (as all smooth and concave trace-form entropies) it exhibits some properties allowing it to be a possible candidate for a generalized quantum information theory. We then use it to determine the degree of entanglement. The influence of the parameter κ, that underpins Kaniadakis entropy, on the mutual information measure is then highlighted. It is shown that Kaniadakis entropy reduces the mutual information, which is always smaller than its usual von Neumann counterpart. Our results may contribute to the ongoing investigation involving generalized entropies in the context of quantum information.

Quantum entanglement and Kaniadakis entropy

In many quantum gravity theories, there is the emergence of a generalized uncertainty principle (GUP), implying a minimal length of the order of the Planck length. From the statistical mechanics point of view, this prescription enters into the phase space structure by modifying the elementary cell volume, which becomes momentum-dependent. In this letter, it is pointed out that if one assumes that the total phase space volume is not affected by the minimum length prescription, the statistics that maximize the entropy are non-Gaussian but exhibit a quadratic correction over Gaussian statistics. The departure from Gaussian statistics is significant for high energies. To substantiate our point, we apply these statistics to the Unruh effect and the Jeans gravitational instability and show that—in these cases—non-Gaussian statistics produce the same effect as the GUP and capture the underlying physics behind it.

Kamel Ourabah

Papers

Planck radiation law and Einstein coefficients reexamined in Kaniadakis κ statistics.

Quantum ion-acoustic solitary waves: the effect of exchange correlation.

Nonthermal and suprathermal distributions as a consequence of superstatistics.

Quantum entanglement and Kaniadakis entropy

Non-Gaussian statistics from the generalized uncertainty principle