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Since its emergence, quantum mechanics has been a challenge for an understanding of reality which is based on our intuition in a classical world. Nevertheless, it has often been tried to impose this understanding of reality on quantum…
We show that the main difference between classical and quantum systems can be understood in terms of information entropy. Classical systems can be considered the ones where the internal dynamics can be known with arbitrary precision while…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
The nature of a physical law is examined, and it is suggested that there may not be any fundamental dynamical laws. This explains the intrinsic indeterminism of quantum theory. The probabilities for transition from a given initial state to…
Throughout quantum mechanics there is statistical balance, in the collective response of an ensemble of systems to differing measurement types. Statistical balance is a core feature of quantum mechanics, underlying quantum mechanical…
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for…
Based on the Bohr's correspondence principle it is shown that relativistic mechanics and quantum mechanics may be considered as generalizations of classical mechanics. A comparative description of relativistic and classical mechanics is…
The purpose of this work is to discuss recent progress in deriving the fundamental laws of thermodynamics (0th, 1st and 2nd-law) from nonequilibrium quantum statistical mechanics. Basic thermodynamic notions are clarified and different…
In recent years a statistical mechanics description of particles, fields and spacetime based on the concept of quantum open systems and the influence functional formalism has been introduced. It reproduces in full the established theory of…
Common observations of the unpredictability of human behavior and the influence of one question on the answer to another suggest social science experiments are probabilistic and may be mutually incompatible with one another, characteristics…
Identical classical particles are distinguishable. This distinguishability affects the number of ways W a macrostate can be realized on the micro-level, and from the relation S = k ln W leads to a non-extensive expression for the entropy.…
Combining intuitive probabilistic assumptions with the basic laws of classical thermodynamics, using the latter to express probabilistic parameters in terms of the thermodynamic quantities, we get a simple unified derivation of the…
Statistical functions such as the moment-generating function, characteristic function, cumulant-generating function, and second characteristic function are cornerstone tools in classical statistics and probability theory. They provide a…
We consider the canonical ensemble of $N$ particles admitting a strange Hamiltonian description. Each of the particles obeys a set of Newtonian equation of motion, which can also be described by the standard canonical Hamiltonian mechanics.…
The classical limit of quantum mechanics is investigated, by focusing on the study of the center of mass of a many-body system where each particle is described by quantum mechanics. We study how, in the limit when the number of particles…
Do scientific theories limit human knowledge? In other words, are there physical variables hidden by essence forever? We argue for negative answers and illustrate our point on chaotic classical dynamical systems. We emphasize parallels with…
Recently, a geometric embedding of the classical space and classical phase space of an n-particle system into the space of states of the system was constructed and shown to be physically meaningful. Namely, the Newtonian dynamics of the…
Some of the problems connected with the interpretation of quantum mechanics are enumerated, in particular those related to some well known paradoxes and, above all, to the measurement process. We then show how the so called "Physics…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
The basic concepts of classical mechanics are given in the operator form. The dynamical equation for a hybrid system, consisting of quantum and classical subsystems, is introduced and analyzed in the case of an ideal nonselective…