Related papers: Composition schemes: q-enumerations and phase tran…
We analyse q-functional equations arising from tree-like combinatorial structures, which are counted by size, internal path length, and certain generalisations thereof. The corresponding counting parameters are labelled by a positive…
Most elemental metals under ambient conditions adopt simple structures such as BCC, FCC and HCP in specific groupings across the Periodic Table, and on compression, many of these elements undergo transitions to surprisingly complex…
We present some product representations for random variables with the Linnik, Mittag-Leffler and Weibull distributions and establish the relationship between the mixing distributions in these representations. Based on these representations,…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
We propose a generalisation of Gibbs' statistical mechanics into the domain of non-negligible phase space correlations. Derived are the probability distribution and entropy as a generalised ensemble average, replacing…
We study a $q$-deformed random unitary ensemble associated with the little-$q$ Laguerre weight, which provides a discrete analogue of the classical Laguerre unitary ensemble. In the double scaling regime $q=e^{-\lambda/N}$, where $N$ is the…
The presence of a phase transition in a finite system can be deduced, together with its order, from the shape of the distribution of the order parameter. This issue has been extensively studied in multifragmentation experiments, with…
A plethora of natural, artificial and social systems exist which do not belong to the Boltzmann-Gibbs (BG) statistical-mechanical world, based on the standard additive entropy $S_{BG}$ and its associated exponential BG factor. Frequent…
Spontaneous symmetry breaking is related to the appearance of emergent phenomena, while a non-vanishing order parameter has been viewed as the sign of turning into such symmetry breaking phase. Recently, we have proposed a continuous…
This paper describes perturbative framework, on the basis of closed-time-path formalism, for studying quasiuniform relativistic quantum field systems near equilibrium and nonequilibrium quasistationary systems. At the first part, starting…
We investigate the continuum q-Potts model at its transition point from the disordered to the ordered regime, with particular emphasis on the coexistence of disordered and ordered phases in the high-q case. We argue that occurrence of phase…
Statistical laws describe regular patterns observed in diverse scientific domains, ranging from the magnitude of earthquakes (Gutenberg-Richter law) and metabolic rates in organisms (Kleiber's law), to the frequency distribution of words in…
High dimensional superposition models characterize observations using parameters which can be written as a sum of multiple component parameters, each with its own structure, e.g., sum of low rank and sparse matrices, sum of sparse and…
We study a model of spatial random permutations over a discrete set of points. Formally, a permutation $\sigma$ is sampled proportionally to the weight $\exp\{-\alpha \sum_x V(\sigma(x)-x)\},$ where $\alpha>0$ is the temperature and $V$ is…
Quantum Phase Transition (QPT) is a phase transition between different quantum states by adjusting some control parameters. Based on the Principle of Hamilton Dynamics (PHD) and the Principle of Lagrangian Dynamics (PLD), a general QPT…
We show that a quantum state may be represented as the sum of a joint probability and a complex quantum modification term. The joint probability and the modification term can both be observed in successive projective measurements. The…
We study the possibility of applying statistical mechanics to generally covariant quantum theories with a vanishing Hamiltonian. We show that (under certain appropiate conditions) this makes sense, in spite of the absence of a notion of…
Some mathematical theories in physics justify their explanatory superiority over earlier formalisms by the clarity of their postulates. In particular, axiomatic reconstructions drive home the importance of the composition rule and the…
By incorporating contributions from both the (chromo)electric scale $gT$ and (chromo)magnetic scale $g^2T$, we establish spectral sum rules of quarks for strongly coupled QCD that respect Fermi-Dirac statistics as required by quantum…