Related papers: Classical phase space and statistical mechanics of…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
Where does quantum mechanics part ways with classical mechanics? How does quantum randomness differ fundamentally from classical randomness? We cannot fully explain how the theories differ until we can derive them within a single axiomatic…
The classical and quantum evolution of a generic probability distribution is analyzed. To that end, a formalism based on the decomposition of the distribution in terms of its statistical moments is used, which makes explicit the differences…
The classical-statistical limit of quantum mechanics is studied. It is proved that the limit $\hbar \to 0$ is the good limit for the operators algebra but it si not so for the state compact set. In the last case decoherence must be invoked…
We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated…
Heat can flow from cold to hot at any phase separation. Therefore Lynden-Bell's gravo-thermal catastrophe must be reconsidered. The original objects of Thermodynamics, the separation of phases at first order phase transitions, like boiling…
Mechanics is developed over a differentiable manifold as space of possible positions. Time is considered to fill a one--dimensional Riemannian manifold, so having the metric as lapse. Then the system is quantized with covariant instead of…
Quantum mechanics is essentially a statistical theory. Classical mechanics, however, is usually not viewed as being inherently statistical. Nevertheless, the latter can also be formulated statistically. Furthermore, a statistical…
Spatial correlations of occupation probabilities, if their decay is not too fast, can change the critical exponents for classical percolation. From numerical studies of electron dynamics in the lowest Landau level (LLL) we demonstrate the…
We compare the classical and quantum mechanical position-space probability densities for a particle in an asymmetric infinite well. In an idealized system with a discontinuous step in the middle of the well, the classical and quantum…
The thermodynamic of particles with intermediate statistics interpolating between Bose and Fermi statistics is adressed in the simple case where there is one quantum number per particle. Such systems are essentially one-dimensional. As an…
We show that QM can be represented as a natural projection of a classical statistical model on the phase space $\Omega= H\times H,$ where $H$ is the real Hilbert space. Statistical states are given by Gaussian measures on $\Omega$ having…
A simple probabilistic cellular automaton is shown to be equivalent to a relativistic fermionic quantum field theory with interactions. Occupation numbers for fermions are classical bits or Ising spins. The automaton acts deterministically…
A recently introduced effective quantum potential theory is studied in a low momentum region of phase space. This low momentum approximation is used to show that the new effective quantum potential induces a space-dependent mass and a…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…
Many quantization schemes rely on analogs of classical mechanics where the connections with classical mechanics are indirect. In this work I propose a new and direct connection between classical mechanics and quantum mechanics where the…
The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…
We discuss the classical and quantum reduction to the space of physical degrees of freedom of Yang--Mills theory on a circle (so that space-time is a cylinder). Although the classical reduced phase space is finite-dimensional, the quantum…
A critical examination of some basic conceptual issues in classical statistical mechanics is attempted, with a view to understanding the origins, structure and statuts of that discipline. Due attention is given to the interplay between…
We study information measures in quantu mechanics, with particular emphasis on providing a quantification of the notions of classicality and predictability. Our primary tool is the Shannon - Wehrl entropy I. We give a precise criterion for…