Related papers: Extensive statistical mechanics based on nonadditi…
We addressed the problem of generalizing the extensive postulates of the standard thermodynamics in order to extend it to the study of nonextensive systems. We did it in analogy with the traditional analysis, starting from the…
Gibbs-Boltzmann entropy leads to systems that have a strong dependence on initial conditions. In reality, most materials behave quite independently of initial conditions. Nonextensive entropy or Tsallis entropy leads to nonextensive…
It is shown by simple and straightforward considerations that discreteness of basic physical variables is, at least, essential for generalized statistical mechanics with non-logarithmic entropy to be thermodynamically applicable to…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble, whereas canonical ones fail in the most interesting, mostly inhomogeneous, situations like phase separations or away from the thermodynamic…
We consider an isolated system in an arbitrary state and provide a general formulation using first principles for an additive and non-negative statistical quantity that is shown to reproduce the equilibrium thermodynamic entropy of the…
A thermodynamic expression for the analog of the canonical ensemble for nonequilibrium systems is described based on a purely information theoretical interpretation of entropy. As an application, it is shown that this nonequilibrium…
Thermodynamics makes definite predictions about the thermal behavior of macroscopic systems in and out of equilibrium. Statistical mechanics aims to derive this behavior from the dynamics and statistics of the atoms and molecules making up…
This work investigates a quantum system described by a Hamiltonian operator in a two dimensional noncommutative space. The system consists of an electron subjected to a perpendicular magnetic field $\mathbf{B}$, coupled to a harmonic…
The nonextensivity in a non-isothermal plasma system with the Coulombian long-range interactions is studied in the framework of Tsallis statistics. We present for first time a mathematical expression of the nonextensive parameter q based on…
The framework of non-extensive statistical mechanics, proposed by Tsallis, has been used to describe a variety of systems. The non-extensive statistical mechanics is usually introduced in a formal way, thus simple models exhibiting some…
We describe some recent applications of Tsallis statistics in fully developed hydrodynamic turbulence and high energy physics. For many of these applications nonextensive properties arise from spatial fluctuations of the temperature or the…
For more than 100 years, one of the central concepts in statistical mechanics has been the microcanonical ensemble, which provides a way of calculating the thermodynamic entropy for a specified energy. A controversy has recently emerged…
Statistical mechanics is generalized on the basis of an information theory for inexact or incomplete probability distributions. A parameterized normalization is proposed and leads to a nonextensive entropy. The resulting incomplete…
In the case of a system with an unbounded hamiltonian the entropic index q of non-extensive thermodynamics has an upperbound q_c>1 beyond which the formalism becomes meaningless. The expression 1/(q_c-1) is the dimension of the state space…
Maximum-entropy ensembles are key primitives in statistical mechanics from which thermodynamic properties can be derived. Over the decades, several approaches have been put forward in order to justify from minimal assumptions the use of…
A classical (non-quantum-mechanical) relativistic ideal gas in thermodynamic equilibrium in a uniformly accelerated frame of reference is studied using Gibbs's microcanonical and grand canonical formulations of statistical mechanics. Using…
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…
Nonadditive composition rules for several physical quantities are treated in thermodynamics. It is argued that the zeroth law defines the existence of their additive forms, the formal logarithms. A further principle, the universal…
Tsallis has proposed a generalisation of the standard entropy, which has since been applied to a variety of physical systems. In the canonical ensemble approach that is mostly used, average energy is given by an unnromalised, or normalised,…
We present an argument which purports to show that the use of the standard Legendre transform in non-additive Statistical Mechanics is not appropriate. For concreteness, we use as paradigm, the case of systems which are conjecturally…