Related papers: Probability distributions in statistical ensembles…
If the prior probability distributions of all possible hypothetical true means and all possible observed means of a continuous variable are conditional on the universal set of all numbers (i.e., before the nature of a study is known and a…
The grand canonical ensemble has been used to make predictions for composite yields using simple models for nuclear fragmentation. While this gives correct model prediction for high energy collisions, it can give very inaccurate results at…
The possibility of reconciliation between canonical probability distributions obtained from the $q$-maximum entropy principle with predictions from the law of large numbers when empirical samples are held to the same constraints, is…
We review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities…
In this paper, we study a distribution of labeled particles on a continuous ring. It arises in three different ways, all related to the multi-type TASEP on a ring. We prove formulas for the probability density function for some permutations…
We investigate the relation between various statistical ensembles of finite systems. If ensembles differ at the level of fluctuations of the order parameter, we show that the equations of states can present major differences. A sufficient…
A simple position probability density formulation is presented for the motion of a particle in a spherically symmetric potential. The approach provides an alternative to Newtonian methods for presentation in an elementary course, and…
This paper considers the problem of distinguishing between classical and quantum domains in macroscopic phenomena using tests based on probability and it presents a condition on the ratios of the outcomes being the same (Ps) to being…
A new ensemble interpretation of quantum mechanics is proposed according to which the ensemble associated to a quantum state really exists: it is the ensemble of all the systems in the same quantum state in the universe. Individual systems…
Distributions of abundances or frequencies play an important role in many fields of science, from biology to sociology, as does the R\'enyi entropy, which measures the diversity of a statistical ensemble. We derive a mathematical relation…
One of the main concepts in quantum physics is a density matrix, which is a symmetric positive definite matrix of trace one. Finite probability distributions are a special case where the density matrix is restricted to be diagonal. Density…
Tsallis has suggested a nonextensive generalization of the Boltzmann-Gibbs entropy, the maximization of which gives a generalized canonical distribution under special constraints. In this brief report we show that the generalized canonical…
In the framework of the Gibbs statistical theory, the question of the size of the particles forming the statistical system is investigated. This task is relevant for a wide variety of applications. The distribution for particle sizes and…
A distribution of electromagnetic fields presents a statistical assembly of a particular type, which is at scale h a quantum statistical assembly itself and has also been instrumental to concretisation of the basic probability assumption of…
In systems with long-range interactions, since energy is a non-additive quantity, ensemble inequivalence can arise: it is possible that different statistical ensembles lead to different equilibrium descriptions, even in the thermodynamic…
Categorical random variables are a common staple in machine learning methods and other applications across disciplines. Many times, correlation within categorical predictors exists, and has been noted to have an effect on various algorithm…
We derive some Quantum Central Limit Theorems for expectation values of macroscopically coarse-grained observables, which are functions of coarse-grained hermitean operators. Thanks to the hermicity constraints, we obtain positive-definite…
A density matrix $\rho$ may be represented in many different ways as a mixture of pure states, $\rho = \sum_i p_i |\psi_i\ra \la \psi_i|$. This paper characterizes the class of probability distributions $(p_i)$ that may appear in such a…
We show that big bang cosmology implies a high degree of entanglement of particles in the universe. In fact, a typical particle is entangled with many particles far outside our horizon. However, the entanglement is spread nearly uniformly…
I discuss the effects of fermionic condensation in systems of constant density of states. I show that the condensation leads to a correction of the chemical potential and of the Fermi distribution in canonical Fermi systems at low…