Related papers: Some Open Points in Nonextensive Statistical Mecha…
This is a survey of topological properties of open, complete nonpositively curved manifolds which may have infinite volume. Topics include topology of ends, restrictions on the fundamental group, as well as a review of known examples.
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, using the maximization of entropy. In…
This paper reviews developments in statistics for spatial point processes obtained within roughly the last decade. These developments include new classes of spatial point process models such as determinantal point processes, models…
Recent theoretical studies of statistical mechanical properties of systems with long range interactions are briefly reviewed. In these systems the interaction potential decays with a rate slower than 1/r^d at large distances r in d…
Further formulas are presented involving quantum mechanics, thermodynamics, and integrable systems. Modifications of dispersionless theory are developed.
Nonextensive statistics is a formalism of statistical mechanics that describes the ocurrence of power-law distributions in complex systems, particularly the so-called $q$ exponential family of distributions. In this work we present the use…
This paper is mainly about the areas of non-Newtonian fluid mechanics which are not investigated or not appropriately and sufficiently investigated. In fact, this should also include emerging areas of research in the field of non-Newtonian…
The non-extensive statistical mechanics has been applied to describe a variety of complex systems with inherent correlations and feedback loops. Here we present a dynamical model based on previously proposed static model exhibiting in the…
Some known fixed point theorems for nonexpansive mappings in metric spaces are extended here to the case of primitive uniform spaces. The reasoning presented in the proofs seems to be a natural way to obtain other general results.
I give a concise introduction to some essential concepts of statistical mechanics: 1. Probability theory (constrained distributions, concentration theorem, frequency estimation, hypothesis testing); 2. Macroscopic systems in equilibrium…
We discuss several open problems on spectrally bounded operators, some new, some old, adding in a few new insights.
Statistical mechanics of the discrete nonlinear Schr\"odinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for…
Recent investigations call attention to the dynamics of anomalous diffusion and its connection with basic principles of statistical mechanics. We present here a short review of those ideas and their implications.
The free scalar field is studied on the Y-junction of three semi infinite axes which is the simplest example of a non-manifold space. It is shown that under an assumption that the junction point can not gain a macroscopic amount of energy…
We develop a general formulation of quantum statistical mechanics in terms of probability currents that satisfy continuity equations in the multi-particle position space, for closed and open systems with a fixed number of particles. The…
Boltzmann-Gibbs statistical mechanics is based on the entropy $S_{BG}=-k \sum_{i=1}^W p_i \ln p_i$. It enables a successful thermal approach of ubiquitous systems, such as those involving short-range interactions, markovian processes, and,…
Long sequences of successive direct (projective) measurements or observations of a few "uninteresting" physical quantities of a quantum system may reveal indirect, but precise and unambiguous information on the values of some very…
The recent progresses in Machine Learning opened the door to actual applications of learning algorithms but also to new research directions both in the field of Machine Learning directly and, at the edges with other disciplines. The case…
The topic of statistical inference for dynamical systems has been studied extensively across several fields. In this survey we focus on the problem of parameter estimation for non-linear dynamical systems. Our objective is to place results…
Superstatistics are superpositions of different statistics relevant for driven nonequilibrium systems with spatiotemporal inhomogeneities of an intensive variable (e.g., the inverse temperature). They contain Tsallis statistics as a special…