Related papers: Thermodynamic Limits, Non-commutative Probability,…
We propose a system of equations to describe the interaction of a quasiclassical variable $X$ with a set of quantum variables $x$ that goes beyond the usual mean field approximation. The idea is to regard the quantum system as continuously…
The interpretation of quantum theory is one of the longest-standing debates in physics. Type I interpretations see quantum probabilities as determined by intrinsic properties of the observed system. Type II see them as relational…
Considering the recently established arbitrariness the Schroedinger equation has to be interpreted as an equation of motion for a statistical ensemble of particles. The statistical qualities of individual particles derive from the unknown…
In this paper, we define a quantum analogue of the notion of empirical measure in the classical mechanics of $N$-particle systems. We establish an equation governing the evolution of our quantum analogue of the $N$-particle empirical…
The thermodynamic limit of the internal energy and the entropy of the system of quantum interacting particles in random medium is shown to exist under the crucial requirements of stability and temperedness of interactions. The energy turns…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
Quantum measurement is ultimately a physical process, resulting from an interaction between the measured system and a measuring apparatus. Considering the physical process of measurement within a thermodynamic context naturally raises the…
We take the view that physical quantities are values generated by processes in measurement, not pre-existent objective quantities, and that a measurement result is strictly a product of the apparatus and the subject of the measurement. We…
Using the kinematic constraints of classical bodies we construct the allowable wavefunctions corresponding to classical solids. These are shown to be long lived metastable states that are qualitatively far from eigenstates of the true…
Entanglement is generally considered necessary for achieving the Heisenberg limit in quantum metrology. We construct analogues of Dicke and GHZ states on a single $N+1$ dimensional qudit that achieve precision equivalent to symmetrically…
We discuss the thermodynamic limit in the canonical area ensemble used in loop quantum gravity to model quantum black holes. The computation of the thermodynamic limit is the rigorous way to obtain a smooth entropy from the counting entropy…
We investigate theoretically the emergence of classical statistical physics in a finite quantum system that is either totally isolated or otherwise subjected to a quantum measurement process. We show via a random matrix theory approach to…
Simulations are performed of a small quantum system interacting with a quantum environment. The system consists of various initial states of two harmonic oscillators coupled to give normal modes. The environment is "designed" by its level…
It is common to model random errors in a classical measurement by the normal (Gaussian) distribution, because of the central limit theorem. In the quantum theory, the analogous hypothesis is that the matrix elements of the error in an…
The continuous quantum measurement within the probability representation of quantum mechanics is discussed. The partial classical propagator of the symplectic tomogram associated to a particular measurement outcome is introduced, for which…
In a previous paper, we have developed a general theory of thermodynamic limits. We apply it here to three different Coulomb quantum systems, for which we prove the convergence of the free energy per unit volume. The first system is the…
Both classical and respectively quantum observables can be modeled as somewhat similar examples of random variables. In such a model the associated measurements preserve the values spectrum of an observable but change the corresponding…
Focusing on isolated macroscopic systems, described either in terms of a quantum mechanical or a classical model, our two key questions are: In how far does an initial ensemble (usually far from equilibrium and largely unknown in detail)…
Thermodynamics of chemical elements, based on the two-component electron-nuclear plasma model shows that the critical parameters for the liquid-vapor transition are the quantum values for which the classical limit is absent.
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…