On some special cases of the Entropy Photon-Number Inequality

We show that the Entropy Photon-Number Inequality (EPnI) holds where one of the input states is the vacuum state and for several candidates of the other input state that includes the cases when the state has the eigenvectors as the number states and either has only two non-zero eigenvalues or has arbitrary number of non-zero eigenvalues but is a high entropy state. We also discuss the conditions, which if satisfied, would lead to an extension of these results.Comment: 12 pages, no figure

Global Income Inequality and Savings: A Data Science Perspective

A society or country with income equally distributed among its people is truly a fiction! The phenomena of socioeconomic inequalities have been plaguing mankind from times immemorial. We are interested in gaining an insight about the co-evolution of the countries in the inequality space, from a data science perspective. For this purpose, we use the time series data for Gini indices of different countries, and construct the equal-time cross-correlation matrix. We then use this to construct a similarity matrix and generate a map with the countries as different points generated through a multi-dimensional scaling technique. We also produce a similar map of different countries using the time series data for Gross Domestic Savings (% of GDP). We also pose a different, yet significant, question: Can higher savings moderate the income inequality? In this paper, we have tried to address this question through another data science technique - linear regression, to seek an empirical linkage between the income inequality and savings, mainly for relatively small or closed economies. This question was inspired from an existing theoretical model proposed by Chakraborti-Chakrabarti (2000), based on the principle of kinetic theory of gases. We tested our model empirically using Gini index and Gross Domestic Savings, and observed that the model holds reasonably true for many economies of the world.Comment: 8 pages, 6 figures. IEEE format. Accepted for publication in 5th IEEE DSAA 2018 conference at Torino, Ital

Anisotropic generalization of well-known solutions describing relativistic self-gravitating fluid systems: An algorithm

We present an algorithm to generalize a plethora of well-known solutions to Einstein field equations describing spherically symmetric relativistic fluid spheres by relaxing the pressure isotropy condition on the system. By suitably fixing the model parameters in our formulation, we generate closed-form solutions which may be treated as anisotropic generalization of a large class of solutions describing isotropic fluid spheres. From the resultant solutions, a particular solution is taken up to show its physical acceptability. Making use of the current estimate of mass and radius of a known pulsar, the effects of anisotropic stress on the gross physical behaviour of a relativistic compact star is also highlighted.Comment: To appear in Eur. Phys. J.