Related papers: Direct derivation of microcanonical ensemble avera…
The one particle quantum mechanics is considered in the frame of a N-body classical kinetics in the phase space. Within this framework, the scenario of a subquantum structure for the quantum particle, emerges naturally, providing an…
We consider ensemble averaged theories with discrete random variables. We propose a suitable measure to do the ensemble average. We also provide a mathematical description of such ensemble averages of theories in terms of Poisson point…
We review here the microcanonical and canonical ensembles constructed on an underlying generalized quantum dynamics and the algebraic properties of the conserved quantities. We discuss the structure imposed on the microcanonical entropy by…
We consider the theory of spontaneous emission for a random medium of stationary two-level atoms. We investigate the dynamics of the field and atomic probability amplitudes for a one-photon state of the system. At long times and large…
We prove two statements about the long time dynamics of integrable Hamiltonian systems. In classical mechanics, we prove the microcanonical version of the Generalized Gibbs Ensemble (GGE) by mapping it to a known theorem and then extend it…
We present an overview of a recently suggested new model of quantum initial conditions for the Universe in the form of a cosmological density matrix. This density matrix originally suggested in the Euclidean quantum gravity framework turns…
We consider the hypothesis that quantum mechanics is an approximation to another, cosmological theory, accurate only for the description of subsystems of the universe. Quantum theory is then to be derived from the cosmological theory by…
Assuming a classical statistical system of point particles the fundamental equations of continuum thermomechanics (continuity equation, equation of motion, and energy equation) shall be derived exactly. The macroscopic state functions…
There is a commonly recognized paradigm in which a multipartite quantum system described by a density matrix having no product eigenbasis is considered to possess nonclassical correlation. Supporting this paradigm, we define two entropic…
The present study regards the zeroth order mean field approximation of a dipole-type interaction model, which is analytically solved in the canonical and microcanonical ensembles. After writing the canonical partition function, the free and…
An explicit expression is derived for the statistical description of small quantum systems, which are relatively-weakly and directly coupled to only small parts of their environments. The derived expression has a canonical form, but is…
Using a theorem of partial differential equations, we present a general way of deriving the conserved quantities associated with a given classical point mechanical system, denoted by its Hamiltonian. Some simple examples are given to…
In quantum theory, equilibrium statistical mechanics is usually formulated through the canonical ensemble, whose privileged status is tied to the Euclidean continuation of time evolution. The microcanonical ensemble, by contrast, is…
The most efficient MC weights for the calculation of physical, canonical expectation values are not necessarily those of the canonical ensemble. The use of suitably generalized ensembles can lead to a much faster convergence of the…
We derive the continuous canonical distribution only by requiring the extensivity of the mean energy and the multiplicative probabilistic composition rule. The derivation is independent of the thermodynamic limit and moreover it does not…
We present general and rigorous results showing that the microcanonical and canonical ensembles are equivalent at all three levels of description considered in statistical mechanics - namely, thermodynamics, equilibrium macrostates, and…
Employing different statistical ensembles may lead to qualitatively different results concerning averages of physical observables on the mesoscopic scale. Here we discuss differences between the canonical and the grandcanonical ensembles…
One key issue of the foundation of statistical mechanics is the emergence of equilibrium ensembles in isolated and closed quantum systems. Recently, it was predicted that in the thermodynamic ($N\rightarrow\infty$) limit of large quantum…
For substitutional crystalline solids typically referred to classical discrete system under constant composition, macroscopic structure in thermodynamically equilibrium state can be typically obtained through canonical average, where a set…
The path integral over Euclidean geometries for the recently suggested density matrix of the Universe is shown to describe a microcanonical ensemble in quantum cosmology. This ensemble corresponds to a uniform (weight one) distribution in…