Nonextensive Statistical Mechanics Application to Vibrational Dynamics of Protein Folding

The vibrational dynamics of protein folding is analyzed in the framework of Tsallis statistics. We employ exact expressions for classical harmonic oscillators by considering the unnormalized constraints. As q→1, we show that these approximations agree with the result of Gaussian network model.     

Self-affinity and nonextensivity of sunspots

In this paper we study the time series of sunspots by using two different approaches, analyzing its self-affine behavior and studying its distribution. The long-range correlation exponent α has been calculated via Detrended Fluctuation Analysis and the power law vanishes to values greater than 11 years. On the other hand, the distribution of the sunspots obeys a q-exponential decay that suggests a non-extensive behavior. This observed characteristic seems to take an alternative interpretation of the sunspots dynamics. The present findings suggest us to propose a dynamic model of sunspots formation based on a nonlinear Fokker–Planck equation. Therefore its dynamic process follows the generalized thermostatistical formalism.     

Gamma function to Beck–Cohen superstatistics

In this paper, we show a mathematical construction of Beck–Cohen superstatistics in the Bayesian point of view with the help of the two representations of a gamma function. Furthermore, it is shown how some results for superstatistics are related to each other.     

Energy conditions of the f(T,B) gravity dark energy model with the validity of thermodynamics

In this article, the analysis of Tsallis holographic dark energy(which turns into holographic dark energy for a particular choice of positive non-additivity parameter δ) in modified f(T, B) gravity with the validity of thermodynamics and energy conditions for a homogeneous and isotropic FLRW Universe has been studied. The enlightenment of the field equation towards f(T,B)=αT~m+βB~n, made possible by the fact that the model is purely accelerating,corresponds to q=-0.54(Mamon and Das 2017 Eur. Phys.J.C 77 49). The generalized second law of thermodynamics is valid not only for the same temperature inside the horizon, but also for the apparent horizon for a change in temperature. The essential inspiration driving this article is to exhibit the applicability that the holographic dark energy achieved from standard Tsallis holographic dark energy and the components acquired from f(T, B) gravity are identical for the specific bounty of constants. The analysis of energy conditions confirms that the weak energy condition and the null energy condition are fulfilled throughout the expansion, while violation of the strong energy condition validates the accelerated expansion of the Universe.With the expansion, the model becomes a quintessence dominated model. The dominant energy condition is not observed initially when the model is filled with genuine baryonic matter,whereas it appears when the model is in the quintessence dominated era.     

A Generalized Measure of Cumulative Residual Entropy

In this work, we introduce a generalized measure of cumulative residual entropy and study its properties. We show that several existing measures of entropy, such as cumulative residual entropy, weighted cumulative residual entropy and cumulative residual Tsallis entropy, are all special cases of this generalized cumulative residual entropy. We also propose a measure of generalized cumulative entropy, which includes cumulative entropy, weighted cumulative entropy and cumulative Tsallis entropy as special cases. We discuss a generating function approach, using which we derive different entropy measures. We provide residual and cumulative versions of Sharma–Taneja–Mittal entropy and obtain them as special cases this generalized measure of entropy. Finally, using the newly introduced entropy measures, we establish some relationships between entropy and extropy measures.     

Tsallis entropy: how unique?

It is shown how, among a class of generalized entropies, the Tsallis entropy can uniquely be identified by the principles of thermodynamics, the concept of stability, and the axiomatic foundations.Received: 6 May 2003, Accepted: 7 July 2003, Published online: 9 December 2003PACS: 05.20.-y, 05.70.-a, 05.90. + m, 65.40.Gr     

Generalization of the lineshape useful in magnetic resonance spectroscopy

A new lineshape function is derived from the Tsallis distribution to describe electron paramagnetic resonance (EPR) spectra, and possibly nuclear magnetic resonance (NMR) spectra as well. This lineshape generalizes the Gaussian and Lorentzian lineshapes that are widely used in simulations. The main features of this lineshape function are presented: the normalization, moments, and first derivative. A number of experimental EPR spectra are compared with the results of simulations employing the new lineshape function. The results show that the new lineshape often provides a better approximation of the experimental spectrum. It is also shown that the new parameter of the lineshape function can be used to quantify the intermolecular spin-spin interactions.     

Nonextensive treatment of nucleation and growth in a thin layer

In this study, a generalized method based upon nonextensive statistics is presented for nucleation and growth processes in a thin layer between two interfaces. It is shown that the presented mathematical model, which uses an index called the entropic index that measures the nonextensivity of the physical system, successfully deals with the nucleation and growth processes, and works better than Johnson–Mehl–Avrami–Kolmogorov model. The presented model also contains Austin–Rickett model as a special case.     

A variational perturbation approximation method in Tsallis non-extensive statistical physics

For the generalized statistical mechanics based on the Tsallis entropy, a variational perturbation approximation method with the principle of minimal sensitivity is developed by calculating the generalized free energy up to the third order in variational perturbation expansion. The approximation up to the first order amounts to a variational approach which covers the variational method developed by E.K. Lenzi, L.C. Malacarne, R.S. Mendes [Phys. Rev. Lett. 80 (1998) 218] and the approximations up to higher orders can systematically improve variational results. As an illustrated example, the generalized free energy for a classical harmonic oscillator (considered in the Lenzi's joint work) are calculated up to the third order, and the resultant approximations up to the first, second, and third orders are numerically compared with the exact result.     

Investigation of the phase transition at the nematic liquid crystal-wall interface within nonextensivity

In this study, the nematic-isotropic phase transition is investigated for a sample in the shape of a slab of thickness d, using nonextensive formalism. The interaction potential is written as the sum of the direct interaction of a given nematic molecule with the substrate and of its incomplete interaction with the other nematic molecules due to the presence of the limiting surface. In this framework, we show the effects of the nonextensivity on the nematic-isotropic transition at the nematic-wall interface. The generalized model can shed light on the properties of nematic liquid crystal confined in small-scale structures.