Related papers: Generalized Energy Statistics and Kostka--Macdonal…
Here we will embark on a journey starting with some ostensibly inauspicious boxes. Carefully stacking them in different ways yields amazing identities. From humble beginnings at the integer version: `how many steps does it take to get from…
In this paper we present a formula for Macdonald's polynomials for the root system A(n-1) which arises from the representation theory of quantum sl(n). This formula expresses Macdonald's polynomials via (weighted) traces of intertwining…
Inhomogeneous lattice paths are introduced as ordered sequences of rectangular Young tableaux thereby generalizing recent work on the Kostka polynomials by Nakayashiki and Yamada and by Lascoux, Leclerc and Thibon. Motivated by these works…
Interacting systems of particles with generalized statistics are considered on both classical and quantum level. It is shown that all possible quantum states and corresponding processes can be represented in terms of certain specific…
Statistical thermodynamics has a universal appeal that extends beyond molecular systems, and yet, as its tools are being transplanted to fields outside physics, the fundamental question, \textit{what is thermodynamics?}, has remained…
In this note we develop a systematic combinatorial definition for constructed earlier supersymmetric polynomial families. These polynomial families generalize canonical Schur, Jack and Macdonald families so that the new polynomials depend…
We consider partially observable Markov decision processes (POMDPs) with a set of target states and positive integer costs associated with every transition. The traditional optimization objective (stochastic shortest path) asks to minimize…
Certain fluctuations in particle number at fixed total energy lead exactly to a cut-power law distribution in the one-particle energy, via the induced fluctuations in the phase-space volume ratio. The temperature parameter is expressed…
A statistical thermodynamic approach of moving particles forming an elastic body is presented which leads to reveal molecular-mechanical properties of classical and nonextensive dynamical systems. We derive the Boltzmann-Gibbs (BG) entropy…
Motivated by applications to the fractional quantum Hall effect and, in particular, to the Bernevig-Haldane conjectures, we investigates the behavior of Macdonald polynomials under specializations of the form q a t b = 1. Our main focus is…
This paper investigates the combinatorics that gives rise to the Boltzmann probability distribution. Despite being one of the most important distributions in physics and other fields of science, the mathematics of the underlying model of…
The $\epsilon$-expansion of several two-loop self-energy diagrams with different thresholds and one mass are calculated. On-shell results are reduced to multiple binomial sums which values are presented in analytical form.
The pathway model of Mathai (2005) is shown to be inferable from the maximization of a certain generalized entropy measure. This entropy is a variant of the generalized entropy of order 'alpha', considered in Mathai and Rathie (1975), and…
In this work assuming valid the equipartition theorem and using the normalized q-expectation value, we obtain, until first order approximation, the hydrodynamics equation for the generalized statistics. This equations are different from…
When dealing with certain kind of complex phenomena the theoretician may face some difficulties -- typically a failure to have access to information for properly characterize the system -- for applying the full power of the standard…
Superstatistics and Tsallis statistics in statistical mechanics is given an interpretation in terms of Bayesian statistical analysis. Subsequently superstatistics is extended by replacing each component of the conditional and marginal…
Traditional interpretations of probability, whether frequentist or subjective, make no reference to the concept of energy. In this paper, we propose that assigning hypothetical energy levels to the outcomes of a random variable can yield…
Using Okounkov's $q$-integral representation of Macdonald polynomials we construct an infinite sequence $\Omega_1,\Omega_2,\Omega_3,\dots$ of countable sets linked by transition probabilities from $\Omega_N$ to $\Omega_{N-1}$ for each…
We present an ab initio stochastic method for calculating thermal properties of a trapped, 1D Bose-gas covering the whole range from weak to strong interactions. Discretization of the problem results in a Bose-Hubbard-like Hamiltonian,…
A completely new approach to the problem of energy distribution in statistical mechanics is developed that results in a general, combinatorial formula for the density of states. Relying on the approach the energy equipartition principle is…