Related papers: Transformation Relation of Two Descriptive Systems…
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…
One attractive interpretation of quantum mechanics is the ensemble interpretation, where Quantum Mechanics merely describes a statistical ensemble of objects and not individual objects. But this interpretation does not address why the…
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…
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…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
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…
Quantum mechanics and classical statistical mechanics are two physical theories that share several analogies in their mathematical apparatus and physical foundations. In particular, classical statistical mechanics is hallmarked by the…
Quantum Mechanics (QM) is a quantum probability theory based on the density matrix. The possibility of applying classical probability theory, which is based on the probability distribution function(PDF), to describe quantum systems is…
The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical…
Statistical classical mechanics and quantum mechanics are developed and well-known theories that represent a basis for modern physics. The two described theories are well known and have been well studied. As these theories contain numerous…
In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg…
Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a new…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
Experiments violating Bell's inequality appear to indicate deterministic models do not correspond to a realistic theory of quantum mechanics. The theory of pilot waves seemingly overcomes this hurdle via nonlocality and statistical…
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…
Non-relativistic quantum mechanics is reformulated here based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum…
It is proved in the paper that the non-conservative dissipative force and asymmetry of time reversal can be naturally introduced into classical statistical mechanics after retarded electromagnetic interaction between charged microparticles…
Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…
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…