Related papers: Quantum Bose-Einstein Statistics for Indistinguish…
The role of Bose-Einstein correlations in a widely discussed intermittency phenomenon is reviewed. In particular, it is shown that particle correlations of different origin are better displayed when analysed as functions of appropriately…
We study the problem of particle indistinguishability for the three cases known in nature: identical classical particles, identical bosons and identical fermions. By exploiting the fact that different types of particles are associated with…
In the works on Statistical Mechanics and Statistical Physics, when deriving the distribution of particles of ideal gases, one uses the method of Lagrange multipliers in a formal way. In this paper we treat rigorously this problem for…
We review recent results about the maximal values of the Kullback-Leibler information divergence from statistical models defined by neural networks, including naive Bayes models, restricted Boltzmann machines, deep belief networks, and…
We investigate the asymptotic behavior of Bayesian posterior distributions under independent and identically distributed ($i.i.d.$) misspecified models. More specifically, we study the concentration of the posterior distribution on…
We derive a stochastic process that describes the kinetics of a one-dimensional Bose gas in a regime where three body collisions are important. In this situation the system becomes non integrable offering the possibility to investigate…
The emergence of macroscopic coherence in a many-body quantum system is a ubiquitous phenomenon across different physical systems and scales. This Chapter reviews key concepts characterizing such systems (correlation functions,…
The crucial feature of a memoryless stochastic process is that any information about its state can only decrease as the system evolves. Here we show that such a decrease of information is equivalent to the underlying stochastic evolution…
A manifestly covariant relativistic statistical mechanics of the system of $N$ indistinguishable events with motion in space-time parametrized by an invariant ``historical time'' $\tau $ is considered. The relativistic mass distribution for…
Building upon the framework established in our recent work [M. Seifi et al., Phys. Rev. E 111, 054114 (2025)], wherein a generalized Maxwell Boltzmann distribution was formulated using the Mittag Leffler function within the superstatistical…
The Bell inequality is derived under the assumption of three physical data sets, random or deterministic. The data sets represent a laboratory realization of the three probability based variables used by Bell. For physical data as can be…
The aim of this paper is to establish Hoeffding and Bernstein type concentration inequalities for weighted sums of exchangeable random variables. A special case is the i.i.d. setting, where random variables are sampled independently from…
Identifying Bell states without destroying it is frequently dealt with in nowadays quantum technologies such as quantum communication and quantum computing. In practice, quantum entangled states are often distributed among distant parties,…
Nonlinear variants of quantum mechanics can solve tasks that are impossible in standard quantum theory, such as perfectly distinguishing nonorthogonal states. Here we derive the optimal protocol for distinguishing two states of a qubit…
There has been growing interest in recent years in Q-matrix based cognitive diagnosis models. Parameter estimation and respondent classification under these models may suffer due to identifiability issues. Non-identifiability can be…
In this paper we study the entanglement properties of free {\em non-relativistic} Bose gases. At zero temperature, we calculate the bipartite block entanglement entropy of the system, and find it diverges logarithmically with the particle…
This study critically analyses the information-theoretic, axiomatic and combinatorial philosophical bases of the entropy and cross-entropy concepts. The combinatorial basis is shown to be the most fundamental (most primitive) of these three…
In the present work we are studying a bosonic quantum field system at finite temperature, and at zero and non-zero chemical potential. For a simple spatial partition we derive the corresponding mutual information, a quantity that measures…
We discuss the properties of an ideal relativistic gas of events possessing Bose-Einstein statistics. We find that the mass spectrum of such a system is bounded by $\mu \leq m\leq 2M/\mu _K,$ where $\mu $ is the usual chemical potential,…
In Gentile statistics the maximum occupation number can take on unrestricted integers: $1<n<\infty $. It is usually believed that Gentile statistics will reduce to Bose-Einstein statistics when n equals the total number of particles in the…