Nonextensive Tsallis statistics in Unruh effect for Dirac neutrinos

Flavor mixing of quantum fields was found to be responsible for the breakdown of the thermality of Unruh effect. Recently, this result was revisited in the context of nonextensive Tsallis thermostatistics, showing that the emergent vacuum condensate can still be featured as a thermal-like bath, provided that the underlying statistics is assumed to obey Tsallis prescription. This was analyzed explicitly for bosons. Here we extend this study to Dirac fermions and in particular to neutrinos. Working in the relativistic approximation, we provide an effective description of the modified Unruh spectrum in terms of the q-generalized Tsallis statistics, the q-entropic index being dependent on the mixing parameters $$\sin \theta $$ sin θ and $$\Delta m$$ Δ m . As opposed to bosons, we find $$q>1$$ q > 1 , which is indicative of the subadditivity regime of Tsallis entropy. An intuitive understanding of this result is discussed in relation to the nontrivial entangled structure exhibited by the quantum vacuum for mixed fields, combined with the Pauli exclusion principle.

Non-extensive transverse momentum distribution for identified particles at SNN = 7.7, 11.5, 19.6, 27, 39GeV

The transverse momentum distribution of charged particles formed in Au–Au collisions at Beam Energy Scan (BES) ([Formula: see text][Formula: see text]GeV) is investigated. In addition, [Formula: see text] spectra of [Formula: see text] particle at [Formula: see text][Formula: see text]GeV were examined. Tsallis distribution is used to extract the temperature, volume and the entropic index from the experimental results at mid-rapidity and zero chemical potential. We measure some particle ratios like [Formula: see text] and [Formula: see text] which are puzzling horn in the experiment and in the thermal model. We conclude that the horn vanished when we used Tsallis distribution, but this does not confirm a solution to the puzzle, which is primarily visible in the experimental results.

Temperature fluctuations and Tsallis statistics in relativistic heavy ion collisions

In this paper, we study temperature fluctuations in the initial stages of the relativistic heavy ion collision using a multiphase transport model. We consider the plasma in the initial stages after collision before it has a chance to equilibrate. We have considered [Formula: see text] collision with a center-of-mass energy of 200 GeV. We use the nonextensive Tsallis statistics to find the entropic index in the partonic stages of the relativistic heavy ion collisions. We find that the temperature and the entropic index have a linear relationship during the partonic stages of the heavy ion collision. This has already been observed in the hadronic phase. A detailed analysis of the dependence of the entropic index on the system shows that for increasing spacetime rapidity, the entropic index of the partonic system increases. The entropic index also depends on the beam collision energy. The calculation of the entropic index from the experimental data fitting of the transverse momenta deals with the hadronic phase. However, our study shows that the behavior of the entropic index in the initial nonequilibrium stage of the collision is very similar to the behavior of the entropic index in the hadronic stage.

Non-Extensive Statistical Analysis of Acoustic Emissions: The Variability of Entropic Index q during Loading of Brittle Materials until Fracture

Non-extensive statistical mechanics (NESM), introduced by Tsallis based on the principle of non-additive entropy, is a generalisation of the Boltzmann–Gibbs statistics. NESM has been shown to provide the necessary theoretical and analytical implementation for studying complex systems such as the fracture mechanisms and crack evolution processes that occur in mechanically loaded specimens of brittle materials. In the current work, acoustic emission (AE) data recorded when marble and cement mortar specimens were subjected to three distinct loading protocols until fracture, are discussed in the context of NESM. The NESM analysis showed that the cumulative distribution functions of the AE interevent times (i.e., the time interval between successive AE hits) follow a q-exponential function. For each examined specimen, the corresponding Tsallis entropic q-indices and the parameters βq and τq were calculated. The entropic index q shows a systematic behaviour strongly related to the various stages of the implemented loading protocols for all the examined specimens. Results seem to support the idea of using the entropic index q as a potential pre-failure indicator for the impending catastrophic fracture of the mechanically loaded specimens.

Associating an Entropy with Power-Law Frequency of Events

Events occurring with a frequency described by power laws, within a certain range of validity, are very common in natural systems. In many of them, it is possible to associate an energy spectrum and one can show that these types of phenomena are intimately related to Tsallis entropy S q . The relevant parameters become: (i) The entropic index q, which is directly related to the power of the corresponding distribution; (ii) The ground-state energy ε 0 , in terms of which all energies are rescaled. One verifies that the corresponding processes take place at a temperature T q with k T q ∝ ε 0 (i.e., isothermal processes, for a given q), in analogy with those in the class of self-organized criticality, which are known to occur at fixed temperatures. Typical examples are analyzed, like earthquakes, avalanches, and forest fires, and in some of them, the entropic index q and value of T q are estimated. The knowledge of the associated entropic form opens the possibility for a deeper understanding of such phenomena, particularly by using information theory and optimization procedures.