Related papers: What is Statistics?; The Answer by Quantum Languag…
Concepts and formalism from acoustics are often used to exemplify quantum mechanics. Conversely, quantum mechanics could be used to achieve a new perspective on acoustics, as shown by Gabor studies. Here, we focus in particular on the study…
The representation of numbers by product states in quantum mechanics can be extended to the representation of words and word sequences in languages by product states. This can be used to study quantum systems that generate text that has…
Statistical classical mechanics and quantum mechanics are developed and well-known theories that represent a basis for modern physics. The two described theories are well known and have been well studied. As these theories contain numerous…
The relational interpretation (or RQM, for Relational Quantum Mechanics) solves the measurement problem by considering an ontology of sparse relative events, or "facts". Facts are realized in interactions between any two physical systems…
Quantum estimation theory is a reformulation of random statistical theory with the modern language of quantum mechanics. In fact, the density operator plays a role similar to that of probability distribution functions in classical…
The convenience of coherent state representation is discussed from the viewpoint of what is in a broad sense called the measurement problem in quantum mechanics. Standard quantum theory in coherent state representation is intrinsically…
A new, realist interpretation of the quantum measurement processes is given. In this scenario a quantum measurement is a non-equilibrium phase transition in a ``resonant cavity'' formed by the entire physical universe including all its…
In this paper, we propose standard statistical tools as a solution to commonly highlighted problems in the explainability literature. Indeed, leveraging statistical estimators allows for a proper definition of explanations, enabling…
Axiomatic approach to measurement theory is developed. All the possible statistical properties of apparatuses measuring an observable with nondegenerate spectrum allowed in standard quantum mechanics are characterized.
We present a theoretical and empirical investigation of the statistical behaviour of the words in a text produced by human language. To this aim, we analyse the word distribution of various texts of Italian language selected from a specific…
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…
Through extended consideration of two wide classes of case studies -- dilute gases and linear systems -- I explore the ways in which assumptions of probability and irreversibility occur in contemporary statistical mechanics, where the…
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…
We introduce a new mathematical framework for the probabilistic description of an experiment on a system of any type in terms of information representing this system initially. Based on the notions of an information state and a generalized…
The language of operator algebras is of great help for the formulation of questions and answers in quantum statistical mechanics. In Chapter 1 we present a minimal mathematical introduction to operator algebras, with physical applications…
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for…
Quantum cosmology is the quantum theory of the entire universe. Although strange at first sight, it is appropriate because (1) our world appears to be fundamentally quantum, (2) the classical description of gravity breaks down at…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
Invitation to the statistical study of language: The topic of this presentation is the interdisciplinary nexus between linguistics and statistics. It targets linguists, for whom it may have a theoretical interest, or professionals that work…
A major question in our understanding of the fabric of the world is where the randomness of some quantum phenomena comes from and how to represent it in a rational theory. The statistical interpretation of quantum mechanics made its way…