Analogies and Relations between Non-Additive Entropy Formulas and Gintropy.

We explore formal similarities and mathematical transformation formulas between general trace-form entropies and the Gini index, originally used in quantifying income and wealth inequalities. We utilize the notion of gintropy introduced in our earlier works as a certain property of the Lorenz curve drawn in the map of the tail-integrated cumulative population and wealth fractions. In particular, we rediscover Tsallis' q-entropy formula related to the Pareto distribution. As a novel result, we express the traditional entropy in terms of gintropy and reconstruct further non-additive formulas. A dynamical model calculation of the evolution of Gini index is also presented.

Crater formation and deuterium production in laser irradiation of polymers with implanted nano-antennas.

Recent validation experiments on laser irradiation of polymer foils with and without implanted golden nanoparticles are discussed. First we analyze characteristics of craters, formed in the target after its interaction with the laser beam. Preliminary experimental results show significant production of deuterons when both the energy of laser pulse and concentration of nanoparticles are high enough. We consider the deuteron production via the nuclear transmutation reactions p+C→d+X where protons are accelerated by the Coulomb field generated in the target plasma. We argue that maximal proton energy can be above threshold values for these reactions and the deuteron yield may noticeably increase due to presence of nanoparticles.

The Effect of Femtosecond Laser Irradiation and Plasmon Field on the Degree of Conversion of a UDMA-TEGDMA Copolymer Nanocomposite Doped with Gold Nanorods.

In this work, the effects of femtosecond laser irradiation and doping with plasmonic gold nanorods on the degree of conversion (DC) of a urethane dimethacrylate (UDMA)-triethylene glycol dimethacrylate (TEGDMA) nanocomposite were investigated. The UDMA-TEGDMA photopolymer was prepared in a 3:1 weight ratio and doped with dodecanethiol- (DDT) capped gold nanorods of 25 × 75 or 25 × 85 nm nominal diameter and length. It was found that the presence of the gold nanorods alone (without direct plasmonic excitation) can increase the DC of the photopolymer by 6-15%. This increase was found to be similar to what could be achieved with a control heat treatment of 30 min at 180 °C. It was also shown that femtosecond laser impulses (795 nm, 5 mJ pulse energy, 50 fs pulse length, 2.83 Jcm-2 fluence), applied after the photopolymerization under a standard dental curing lamp, can cause a 2-7% increase in the DC of undoped samples, even after thermal pre-treatment. The best DC values (12-15% increase) were obtained with combined nanorod doping and subsequent laser irradiation close to the plasmon resonance peak of the nanorods (760-800 nm), which proves that the excited plasmon field can directly facilitate double bond breakage (without thermoplasmonic effects due to the short pulse length) and increase the crosslink density independently from the initial photopolymerization process.

Kaniadakis Entropy Leads to Particle-Hole Symmetric Distribution.

We discuss generalized exponentials, whose inverse functions are at the core of generalized entropy formulas, with respect to particle-hole (KMS) symmetry. The latter is fundamental in field theory; so, possible statistical generalizations of the Boltzmann formula-based thermal field theory have to take this property into account. We demonstrate that Kaniadakis' approach is KMS ready and discuss possible further generalizations.

Transient Dynamics in the Random Growth and Reset Model.

A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contributes to this direction, studying the transient dynamics in the discrete version of the model by two different approaches. The first method is based on mathematical induction by the recursive integration of the coupled differential equations for the discrete states. The second method transforms the coupled ordinary differential equation system into a partial differential equation for the generating function. We derive analytical results for some important, practically interesting cases and discuss the obtained results for the transient dynamics.

Gintropy: Gini Index Based Generalization of Entropy.

Entropy is being used in physics, mathematics, informatics and in related areas to describe equilibration, dissipation, maximal probability states and optimal compression of information. The Gini index, on the other hand, is an established measure for social and economical inequalities in a society. In this paper, we explore the mathematical similarities and connections in these two quantities and introduce a new measure that is capable of connecting these two at an interesting analogy level. This supports the idea that a generalization of the Gibbs-Boltzmann-Shannon entropy, based on a transformation of the Lorenz curve, can properly serve in quantifying different aspects of complexity in socio- and econo-physics.

Science and Facebook: The same popularity law!

The distribution of scientific citations for publications selected with different rules (author, topic, institution, country, journal, etc…) collapse on a single curve if one plots the citations relative to their mean value. We find that the distribution of "shares" for the Facebook posts rescale in the same manner to the very same curve with scientific citations. This finding suggests that citations are subjected to the same growth mechanism with Facebook popularity measures, being influenced by a statistically similar social environment and selection mechanism. In a simple master-equation approach the exponential growth of the number of publications and a preferential selection mechanism leads to a Tsallis-Pareto distribution offering an excellent description for the observed statistics. Based on our model and on the data derived from PubMed we predict that according to the present trend the average citations per scientific publications exponentially relaxes to about 4.

Dynamical stationarity as a result of sustained random growth.

In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast-growing complex systems. In order to model such phenomena we apply both a discrete and a continuous master equation. The derivation of elementary rates from known stationary distributions is a generalization of the fluctuation-dissipation theorem. Entropic distance evolution is given for such systems. We reconstruct distributions obtained for growing networks, particle production, scientific citations, and income distribution.

Power-law tails from multiplicative noise.

We show that the well-known linear Langevin equation, modeling the Brownian motion and leading to a Gaussian stationary distribution of the corresponding Fokker-Planck equation, is changed by the smallest multiplicative noise. This leads to a power-law tail of the distribution for sufficiently large momenta. At finite ratio of the correlation strength for the multiplicative and the additive noises the stationary energy distribution becomes exactly the Tsallis distribution.