Related papers: Fractal structure and non extensive statistics
A paradigmatic nonhyperbolic dynamical system exhibiting deterministic diffusion is the smooth nonlinear climbing sine map. We find that this map generates fractal hierarchies of normal and anomalous diffusive regions as functions of the…
The theory of superstatistics, originally proposed for the study of complex nonequilibrium systems, has recently been extended to studies of small systems interacting with a finite environment, because such systems display interestingly…
Our previous works have shown the statistical mechanics of self-gravitating system. In this paper, we will show its thermodynamics and compare our results with observations and simulations. We propose that our statistical mechanics can be…
In this work, we present a detailed thermodynamic analysis of a bound quantum system: the Morse oscillator within the framework of Tsallis nonextensive statistics. Using the property of the bound spectrum (upper bound) of the Morse…
We present two issues here: (i) that in situation when total energy is kept constant recently proposed fluctuations of volume ensemble is equivalent to the approach using Tsallis statistics with fluctuating temperature and (ii) that the…
A new statistical approach is presented to study the thermal instability process of optically thin unmagnetized plasma. In this approach the time evolution of mass distribution function over temperature is calculated. This function…
We examine the non-extensive approach to the statistical mechanics of Hamiltonian systems with $H=T+V$ where $T$ is the classical kinetic energy. Our analysis starts from the basics of the formalism by applying the standard variational…
During the past dozen years there have been numerous articles on a relation between entropy and probability which is non-additive and has a parameter $q$ that depends on the nature of the thermodynamic system under consideration. For $q=1$…
It is pointed out that the constraint to be imposed to the maximization of the entropy for processes outside the class of thermodynamical systems, is generally not well defined. In fact, any probability distribution can be derived from…
A new approach to non-extensive thermodynamical systems with non-additive energy and entropy is proposed. The main idea of the paper is based on the statistical matching of the thermodynamical systems with the additive multi-step Markov…
The Boltzmann distribution for an equilibrium system constrains the statistics of the system by the energetics. Despite the non-equilibrium generalization of the Boltzmann distribution being studied extensively, a unified framework valid…
Tsallis' non-extensive statistical mechanics is claimed to be the correct tool to describe the behaviour of low-dimensional dissipative maps at the edge of chaos. Indeed, many different approaches confirm that, for those systems, the…
The theory of mesoscopic fluctuations is applied to inhomogeneous solids consisting of chaotically distributed regions with different crystalline structure. This approach makes it possible to describe statistical properties of such mixture…
Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of…
The non-extensive self-consistent theory describing the thermodynamics of hadronic systems at high temperatures is used to derive some thermodynamical quantities, as pressure, entropy, speed of sound and trace-anomaly. The calculations are…
We show that there exists a natural way to define a condition of generalized thermal equilibrium between systems governed by Tsallis thermostatistics, under the hypotheses that i) the coupling between the systems is weak, ii) the structure…
The work approaches the study of the fluctuations for the thermodynamic systems in the presence of the fields. The approach is of phenomenological nature and developed in a Gaussian approximation. The study is exemplified on the cases of a…
Gibbs and Boltzmann definitions of temperature agree only in the macroscopic limit. The ambiguity in identifying the equilibrium temperature of a finite sized `small' system exchanging energy with a bath is usually understood as a…
We study non-equilibrium statistical mechanics of a Gaussian dynamical system and compute in closed form the large deviation functionals describing the fluctuations of the entropy production observable with respect to the reference state…
In this paper, we study the thermodynamics of quantum harmonic oscillator in the Tsallis framework and in the presence of a minimal length uncertainty. The existence of the minimal length is motivated by various theories such as string…