Related papers: Why are Orlicz spaces useful for Statistical Physi…
In this note we extend two characterizations of admissible operators with respect to $\mathrm{L}^p$ to more general Orlicz spaces. The equivalent conditions are given by the property that an associated operator generates a strongly…
Many statistical issues arise in the analysis of Particle Physics experiments. We give a brief introduction to Particle Physics, before describing the techniques used by Particle Physicists for dealing with statistical problems, and also…
The aim of this note consists of the introduction of unfolding operator in the Orlicz setting.
This work is a conceptual analysis of certain recent developments in the mathematical foundations of Classical and Quantum Mechanics which have allowed to formulate both theories in a common language. From the algebraic point of view, the…
We discuss here the use of generalized forms of entropy, taken as information measures, to characterize phase transitions and critical behavior in thermodynamic systems. Our study is based on geometric considerations pertaining to the space…
The statistical model of quantum mechanics is based on the mapping between operators on the Hilbert space and functions on the phase space. This map can be implemented by an operator that satisfies physically motivated Stratonovich-Weyl…
In the present paper we introduce a certain class of non commutative Orlicz spaces, associated with arbitrary faithful normal locally-finite weights on a semi-finite von Neumann algebra $M.$ We describe the dual spaces for such Orlicz…
This is intended as an analysis of the global properties of static and stationary spacetimes with complete (timelike) Killing field, with particular attention to quotients by group actions. This is presented in terms of algebraic structures…
It is shown how, given a "probability data table" for a quantum or classical system, the representation of states and measurement outcomes as vectors in a real vector space follows in a natural way. Some properties of the resulting sets of…
We use the fact that some linear Hamiltonian systems can be considered as ``finite level'' quantum systems, and the description of quantum mechanics in terms of probabilities, to associate probability distributions with this particular…
In this paper we define bicomplex Orlicz space with hyperbolic valued Luxemburg norm and discussed some of their properties. We have also partially characterize an integral representation of a $\mathbb{D}$-valued convex function. Further we…
The idea of writing a table of probabilistic data for a quantum or classical system, and of decomposing this table in a compact way, leads to a shortcut for Hardy's formalism, and gives new perspectives on foundational issues.
A new class of convex functions called functions, Young functions, strong Young functions and Orlicz functions are introduced by relaxing the definitions of functions, Young functions, strong Young functions and Orlicz functions. Then, new…
We present a general formalism for studying the effects of dynamical heterogeneity in open quantum systems. We develop this formalism in the state space of density operators, on which ensembles of quantum states can be conveniently…
The new scheme employed (throughout the thermodynamic phase space), in the statistical thermodynamic investigation of classical systems, is extended to quantum systems. Quantum Nearest Neighbor Probability Density Functions are formulated…
Classical statistical particle mechanics in the configuration space can be represented by a nonlinear Schrodinger equation. Even without assuming the existence of deterministic particle trajectories, the resulting quantum-like statistical…
Trough the classical umbral calculus, we provide new, compact and easy to handle expressions of k-statistics, and more in general of U-statistics. In addition such a symbolic method can be naturally extended to multivariate case and to…
It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can't contain more…
This paper introduces statistical order convergence and its pointwise variant for sequences of order bounded operators between Riesz spaces. We establish fundamental properties: uniqueness of the limit, stability under lattice operations,…
The new method of multivariate data analysis based on the complements of classical probability distribution to quantum state and Schmidt decomposition is presented. We considered Schmidt formalism application to problems of statistical…