In this article we give a generalization of Hartley's model for the measure of information. We propose a rate of emergence, which is applicable to systems obeying classical or quantum statistics. Quantum systems that obey Fermi-Dirac statistics and Bose-Einstein condensate, as well as classical systems obeying the Maxwell-Boltzmann statistics have been considered. We found that the emergence parameter of quantum and classical systems differ as well as the emergence parameter of quantum systems of fermions and bosons. Consequently, the emergence parameter might be used to distinguish the classical system and quantum system, as well as quantum system of fermions and the quantum system of bosons
In this article we give a generalization of Hartley's model for the measure of information. We propose a rate of emergence, which is applicable to systems obeying classical or quantum statistics. Quantum systems that obey Fermi-Dirac statistics and Bose-Einstein condensate, as well as classical systems obeying the Maxwell-Boltzmann statistics have been considered. We found that the emergence parameter of quantum and classical systems differ as well as the emergence parameter of quantum systems of fermions and bosons. Consequently, the emergence parameter might be used to distinguish the classical system and quantum system, as well as quantum system of fermions and the quantum system of bosons
The case study of fermions and the attempt to deduce their structure from classical probability opens new ways for classical and quantum probability, in particular, for the notion of stochastic coupling which, on the basis of the example of fermions, we enlarge to the notion of algebraic coupling, and for the various notions of stochastic independence. These notions are shown to be strictly correlated with algebraic and stochastic couplings. This approach allows to expand considerably the notion of open system. The above statements will be illustrated with some examples. The last section shows how, from these new stochastic couplings, new statistics emerge alongside the known Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics.
The case study of fermions and the attempt to deduce their structure from classical probability opens new ways for classical and quantum probability, in particular, for the notion of stochastic coupling which, on the basis of the example of fermions, we enlarge to the notion of algebraic coupling, and for the various notions of stochastic independence. These notions are shown to be strictly correlated with algebraic and stochastic couplings. This approach allows to expand considerably the notion of open system. The above statements will be illustrated with some examples. The last section shows how, from these new stochastic couplings, new statistics emerge alongside the known Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics. Bibliography: 5 titles.
We will study fermionic systems like atomic nuclei and bosonic systems like the correlated atoms in a trap from an information-theoretical point of view. The Shannon and Onicescu information measures are calculated for the above systems by comparing the correlated and uncorrelated cases as functions of the strength of the short range correlations. One-body and two-body density and momentum distributions are employed. Thus, the effect of short-range correlations on the information content is evaluated. The magnitude of distinguishability between the correlated and uncorrelated densities is also discussed employing suitable measures for the distance of states i.e. the well known Kullback–Leibler relative entropy and the recently proposed Jensen–Shannon divergence entropy. We will see that the same information-theoretical properties hold for quantum many-body systems obeying Bose–Einstein and Fermi–Dirac (statistics).
All physical systems register bits of information, whether it be an atom, an electrical current, the location of a billiard ball, or a switch. Information can be classical, quantum, or a hybrid of both, depending on the system. For example, an atom or an electron or a superconducting system can register quantum information because the quantum theory applies to each of these systems, but we can safely argue that the location of a billiard ball registers classical information only. These atoms or electrons or superconducting systems can also register classical bits because it is always possible for a quantum system to register classical bits. The term information , in the context of information theory, has a precise meaning that is somewhat different from our prior “everyday” experience with it. Recall that the notion of the physical bit refers to the physical representation of a bit, and the information bit is a measure of how much we learn from the outcome of a random experiment. Perhaps the word “surprise” better captures the notion of information as it applies in the context of information theory. This chapter begins our formal study of classical information. Recall that Chapter 2 reviewed some of the major operational tasks in classical information theory. Here, our approach is somewhat different because our aim is to provide an intuitive understanding of information measures, in terms of the parties who have access to the classical systems. We define precise mathematical formulas that measure the amount of information encoded in a single physical system or in multiple physical systems. The advantage of developing this theory is that we can study information in its own right without having to consider the details of the physical system that registers it. We first introduce the entropy in Section 10.1 as the expected surprise of a random variable. We extend this basic notion of entropy to develop other measures of information in Sections 10.2–10.6 that prove useful as intuitive informational measures, but also, and perhaps more importantly, these measures are the answers to operational tasks that one might wish to perform using noisy resources. While introducing these quantities, we discuss and prove several mathematical results concerning them that are important tools for the practicing information theorist.
A&E Trounev IT Consulting, Toronto, Canada В статье дано системное обобщение формулы Хартли для количества информации . Предложен коэффициент эмерджентности , применимый для систем , подчиняющихся классической или кванто-вой статистике . Дан алгоритм оценки уровня си-стемности квантовых объектов . Рассмотрены кван-товые системы , подчиняющиеся статистике Фер-ми -Дирака и Бозе -Эйнштейна , а также классиче-ские системы подчиняющиеся статистике Макс-велла -Больцмана . Установлено , что коэффициенты эмерджентности квантовых и классических систем отличаются между собой , как и коэффициенты квантовых систем ферми -частиц и бозе -частиц . Следовательно , коэффициент эмерджентности поз-воляет отличить классическую систему от кванто-вой системы , а квантовую систему ферми -частиц от квантовой системы бозе -частиц In this article we give a generalization of Hartley's model for the measure of information. We propose a rate of emergence, which is applicable to systems obeying classical or quantum statistics. Quantum sys-tems that obey Fermi-Dirac statistics and Bose-Einstein condensate, as well as classical systems obey-ing the Maxwell-Boltzmann statistics have been con-sidered. We found that the emergence parameter of quantum and classical systems differ as well as the emergence parameter of quantum systems of fermions and bosons. Consequently, the emergence parameter might be used to distinguish the classical system and quantum system, as well as quantum system of fermi-ons and the quantum system of bosons Ключевые слова : КВАНТОВАЯ СТАТИСТИКА , СТАТИСТИКА ФЕРМИ -ДИРАКА , СТАТИСТИ-КА БОЗЕ -ЭЙНШТЕЙНА , СТАТИСТИКА МАКС-ВЕЛЛА -БОЛЬЦМАНА , СИСТЕМНАЯ ТЕОРИЯ ИНФОРМАЦИИ , ЭМЕРДЖЕНТНОСТЬ Keywords: COMPLEX SYSTEM, EMERGENCE, INFORMATION THEORY, QUANTUM STATIS-TICS, FERMI-DIRAC STATISTICS, BOSE-EINSTEIN STATISTICS, MAXWELL-BOLTZMANN STATISTICS