Related papers: Is the Tsallis q-mean value instable?

In the present paper the conditions for the validity of the Tsallis' Statistics are analyzed. The same has been done following the analogy with the traditional case: starting from the microcanonical description of the systems and taking…

Stabilization is still a somewhat controversial issue concerning its very existence and also the precise conditions for its occurrence. The key quantity to settle these questions is the ionization probability, for which hitherto no…

We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalised to describe…

In spite of its undeniable success, there are still open questions regarding Tsallis non-extensive statistical formalism, whose founding stone was laid in 1988 in JSTAT. Some of them are concerned with the so-called normalization problem of…

In this work, we consider systems that are subjected to intermittent instabilities due to external stochastic excitation. These intermittent instabilities, though rare, have a large impact on the probabilistic response of the system and…

We study the instability of bound states for abstract nonlinear Schr\"{o}dinger equations. We prove a new instability result for a borderline case between stability and instability. We also reprove some known results in a unified way.

By writing total Tsallis entropy as a function of non-extensivity q-parameter withing the fragment-asperity model for earthquakes, a critical range of values is identified: 1.4 <q< 1.8. It comes directly from constructing the non-extensive…

Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…

Statistical description of stochastic dynamics in highly unstable potentials is strongly affected by properties of divergent trajectories, that quickly leave meta-stable regions of the potential landscape and never return. Using ideas from…

In the present work, we have found that the phenomenological Tsallis distribution (which nowadays is largely used to describe the transverse momentum distributions of hadrons measured in $pp$ collisions at high energies) is consistent with…

Based on the spectral decomposition technique, we introduce a simple and universal numerical method to analyze the stability of solitons. Adopting this method, the linear dynamical properties of $Q$-balls are systematically revealed, from…

Tsallis statistics (or q-statistics) in nonextensive statistical mechanics is a one-parameter description of correlated states. In this paper we use a translated entropic index: $1 - q \to q$ . The essence of this translation is to improve…

If the generalized statistics suggested by Tsallis are used in statistical mechanics, the fluctuation-dissipation theorem no longer holds. Only in the limiting case where Boltzmann statistics are recovered is the theorem applicable. In…

The thermodynamic stability condition (TSC) of Tsallis' entropy is revisited. As Ramshaw [Phys. Lett. A {\bf 198} (1995) 119] has already pointed out, the concavity of Tsallis' entropy with respect to the internal energy is not sufficient…

Pattern formation is ubiquitous in nature and the mechanism widely-accepted to underlay them is based on the Turing instability, predicted by Alan Turing decades ago. This is a non-trivial mechanism that involves nonlinear interaction terms…

We show that the function beta(E) derived from the density of states of a constant heat capacity reservoir coupled to some system of interest is not identical to the physically measurable (transitive) temperature. There are, however,…

We study the problem of mean-square exponential incremental stabilization of nonlinear systems over uncertain communication channels. We show the ability to stabilize a system over such channels is fundamentally limited and the channel…

We axiomatically characterize the Tsallis entropy of a finite quantum system. In addition, we derive a continuity property of Tsallis entropy. This gives a generalization of the Fannes inequality.

In this paper, several numerical examples to illustrate limitations of Quasi Steady-State (QSS) model in long-term voltage stability analysis are presented. In those cases, the QSS model provided incorrect stability assessment. Causes of…

Examples of joint probability distributions are studied in terms of Tsallis' nonextensive statistics both for correlated and uncorrelated variables, in particular it is explicitely shown how correlations in the system can make Tsallis…