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Register a new userNon extensive statistic of Tsallis in the heartbeat of healthy humans
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Added by
Pavel A. Ritto Mijangos
Publication date
2011
fields
Physics
and research's language is
English
Authors
P. A. Ritto
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It is studied the MIT-BIH Normal Sinus Rhythm Database using a statistical technique of analysis, that is based on the Wavelet and Hilbert Transforms. With that technique, it was previously found, that there is a collective and intrinsic dynamical behavior up to a scale of 64 heartbeats. Now it is shown, that using the Biorthogonal wavelet bior3.1 such a behavior reaches the scale 1024. That result confirms, that the circulatory system is out of equilibrium. According to the Statistical Mechanics of Tsallis, and a recent interpretation of G. Wilk et al. respect to the non extensive parameter q, the healthy human being is characterized by q=1.70+/-0.01.
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The speed of sound ($c_s$) is studied to understand the hydrodynamical evolution of the matter created in heavy-ion collisions. The quark-gluon plasma (QGP) formed in heavy-ion collisions evolves from an initial QGP to the hadronic phase via a possible mixed phase. Due to the system expansion in a first order phase transition scenario, the speed of sound reduces to zero as the specific heat diverges. We study the speed of sound for systems, which deviate from a thermalized Boltzmann distribution using non-extensive Tsallis statistics. In the present work, we calculate the speed of sound as a function of temperature for different $q$-values for a hadron resonance gas. We observe a similar mass cut-off behaviour in non-extensive case for $c^{2}_s$ by including heavier particles, as is observed in the case of a hadron resonance gas following equilibrium statistics. Also, we explicitly present that the temperature where the mass cut-off starts, varies with the $q$-parameter which hints at a relation between the degree of non-equilibrium and the limiting temperature of the system. It is shown that for values of $q$ above approximately 1.13 all criticality disappear in the speed of sound, i.e. the decrease in the value of the speed of sound, observed at lower values of $q$, disappears completely.
The nuclear modification factor is derived using Tsallis non-extensive statistics in relaxation time approximation. The variation of nuclear modification factor with transverse momentum for different values of non-extensive parameter, $q$, is also observed. The experimental data from RHIC and LHC are analysed in the framework of Tsallis non-extensive statistics in a relaxation time approximation. It is shown that the proposed approach explains the $R_{AA}$ of all particles over a wide range of transverse momenta but doesnt seem to describe the rise in $R_{AA}$ at very high transverse momenta.
We define an entropy based on a chosen governing probability distribution. If a certain kind of measurements follow such a distribution it also gives us a suitable scale to study it with. This scale will appear as a link function that is applied to the measurements. A link function can also be used to define an alternative structure on a set. We will see that generalized entropies are equivalent to using a different scale for the phenomenon that is studied compared to the scale the measurements arrive on. An extensive measurement scale is here a scale for which measurements fulfill a memoryless property. We conclude that the alternative algebraic structure defined by the link function must be used if we continue to work on the original scale. We derive Tsallis entropy by using a generalized log-logistic governing distribution. Typical applications of Tsallis entropy are related to phenomena with power-law behaviour.
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