Related papers: Statistical Physics in a Finite Volume with Absolu…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
Recursion formulae of the N-particle partition function, the occupation numbers and its fluctuations are given using the single-particle partition function. Exact results are presented for fermions and bosons in a common one-dimensional…
The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since…
In the present article a new method of deriving integral representations of combinations and partitions in terms of harmonic products has been established. This method may be relevant to statistical mechanics and to number theory.
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…
A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
We discuss the quantum statistical fluctuations of energy in subsystems of hot relativistic gas for both spin-zero and spin half particles. We explicitly show the system size dependence of the quantum statistical fluctuation of energy. Our…
Aggregation processes with an arbitrary number of conserved quantities are investigated. On the mean-field level, an exact solution for the size distribution is obtained. The asymptotic form of this solution exhibits nontrivial ``double''…
The Grothendieck and Artin-Mumford exact sequences for the Brauer group of a function field in 1 or 2 variables are applied to derive reciprocity laws for $q$th power residues.
A method of quantum tomography of arbitrary spin particle states is developed on the basis of the root approach. It is shown that the set of mutually complementary distributions of angular momentum projections can be naturally described by…
The partition function of a system of galaxies in gravitational interaction can be cast in an Ising Model form, and this reformulated via a Hubbard--Stratonovich transformation into a three dimensional stochastic and classical scalar field…
Dynamics of the structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The expression…
Based on the concept of ensemble, it is proved in the manuscript that the probability amplitude function can also been used to describe the classical statistical system. The motion equations of probability amplitude functions of classical…
Considering a discrete and finite statistical model of a general position we introduce an exact expression for the partition function in terms of a finite series. The leading term in the series is the Bethe-Peierls (Belief Propagation)-BP…
We propose that observables in quantum theory are properly understood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical…
We present Euler-type recurrence relations for some partition functions. Some of our results provide new recurrences for the number of unrestricted partitions of $n$, denote by $p(n)$. Others establish recurrences for partition functions…
We discuss the problem of the separation of total correlations in a given quantum state into entanglement, dissonance, and classical correlations using the concept of relative entropy as a distance measure of correlations. This allows us to…
Statistical mechanics and thermodynamics for ideal fractional exclusion statistics with mutual statistical interactions is studied systematically. We discuss properties of the single-state partition functions and derive the general form of…
We provide an overview of a canonical formalism that describes mixed quantum-classical systems in terms of statistical ensembles on configuration space, and discuss applications to measurement theory. It is shown that the formalism allows a…