Expected utility maximization problem is one of the most useful tools in mathematical finance, decision analysis and economics. Motivated by statistical model selection, via the principle of expected utility maximization, Friedman and Sandow (J Mach Learn Res 4:257–291, 2003a) considered the model performance question from the point of view of an investor who evaluates models based on the performance of the optimal strategies that the models suggest. They interpreted their performance measures in information theoretic terms and provided new generalizations of (...) Shannon entropy and Kullback–Leibler relative entropy and called them U-entropy and U-relative entropy. In this article, a utility-based criterion for independence of two random variables is defined. Then, Markov’s inequality for probabilities is extended from the U-entropy viewpoint. Moreover, a lower bound for the U-relative entropy is obtained. Finally, a link between conditional U-entropy and conditional Renyi entropy is derived. (shrink)

This article argues that the causal loops that occur in some time-travel scenarios and in certain solutions of the theory of relativity are no more mysterious than the infinitely descending causal chains familiar from Newtonian mechanics.

This paper puts forward an ontology that is indebted to QBism, Kant, Bohr, Schrödinger, the philosophy of the Upanishads, and the evolutionary philosophy of Sri Aurobindo. Central to it is that reality is relative to consciousness or experience. Instead of a single mind-independent reality, there are different poises of consciousness, including a consciousness to which “we are all really only various aspects of the One”. This ontology helps clear up unresolved issues in the philosophy of science, such as arise (...) from the reification of quantum states or from disregard of the universal context of science, which is human experience. It further helps clear up unresolved issues in the philosophy of mind, in particular the problem of intentionality and the dilemma posed by the mutual inclusion of self and world. (shrink)

This paper offers a critique of the Bayesian interpretation of quantum mechanics with particular focus on a paper by Caves, Fuchs, and Schack containing a critique of the “objective preparations view” or OPV. It also aims to carry the discussion beyond the hardened positions of Bayesians and proponents of the OPV. Several claims made by Caves et al. are rebutted, including the claim that different pure states may legitimately be assigned to the same system at the same time, and the (...) claim that the quantum nature of a preparation device cannot legitimately be ignored. Both Bayesians and proponents of the OPV regard the time dependence of a quantum state as the continuous dependence on time of an evolving state of some kind. This leads to a false dilemma: quantum states are either objective states of nature or subjective states of belief. In reality they are neither. The present paper views the aforesaid dependence as a dependence on the time of the measurement to whose possible outcomes the quantum state serves to assign probabilities. This makes it possible to recognize the full implications of the only testable feature of the theory, viz., the probabilities it assigns to measurement outcomes. Most important among these are the objective fuzziness of all relative positions and momenta and the consequent incomplete spatiotemporal differentiation of the physical world. The latter makes it possible to draw a clear distinction between the macroscopic and the microscopic. This in turn makes it possible to understand the special status of measurements in all standard formulations of the theory. Whereas Bayesians have written contemptuously about the “folly” of conjoining “objective” to “probability,” there are various reasons why quantum-mechanical probabilities can be considered objective, not least the fact that they are needed to quantify an objective fuzziness. But this cannot be appreciated without giving thought to the makeup of the world, which Bayesians refuse to do. Doing this on the basis of how quantum mechanics assigns probabilities, one finds that what constitutes the macroworld is a single Ultimate Reality, about which we know nothing, except that it manifests the macroworld or manifests itself as the macroworld. The so-called microworld is neither a world nor a part of any world but instead is instrumental in the manifestation of the macroworld. Quantum mechanics affords us a glimpse “behind” the manifested world, at stages in the process of manifestation, but it does not allow us to describe what lies “behind” the manifested world except in terms of the finished product—the manifested world, for without the manifested world there is nothing in whose terms we could describe its manifestation. (shrink)

Young children help others in a range of situations, relatively indiscriminate of the characteristics of those they help. Recent results have suggested that young children’s helping behaviour extends even to humanoid robots. However, it has been unclear how characteristics of robots would influence children’s helping behaviour. Considering previous findings suggesting that certain robot features influence adults’ perception of and their behaviour towards robots, the question arises of whether young children’s behaviour and perception would follow the same principles. The current study (...) investigated whether two key characteristics of a humanoid robot (animate autonomy and friendly expressiveness) would affect children’s instrumental helping behaviour and their perception of the robot as an animate being. Eighty-two 3-year-old children participated in one of four experimental conditions manipulating a robot’s ostensible animate autonomy (high/low) and friendly expressiveness (friendly/neutral). Helping was assessed in an out-of-reach task and animacy ratings were assessed in a post-test interview. Results suggested that both children’s helping behaviour, as well as their perception of the robot as animate, were unaffected by the robot’s characteristics. The findings indicate that young children’s helping behaviour extends largely indiscriminately across two important characteristics. These results increase our understanding of the development of children’s altruistic behaviour and animate-inanimate distinctions. Our findings also raise important ethical questions for the field of child-robot interaction. (shrink)

This paper introduces a possible alternative model of gravity based on the theory of fractional-dimension spaces and its applications to Newtonian gravity. In particular, Gauss’s law for gravity as well as other fundamental classical laws are extended to a D-dimensional metric space, where D can be a non-integer dimension. We show a possible connection between this Newtonian Fractional-Dimension Gravity (NFDG) and Modified Newtonian Dynamics (MOND), a leading alternative gravity model which accounts for the observed properties of galaxies and other astrophysical (...) structures without requiring the dark matter hypothesis. The MOND acceleration constant $${a_{0}} \simeq 1.2 \times 10^{-10} \text {m}\, \text{s}^{-2}$$ can be related to a natural scale length $$l_{0}$$ in NFDG, i.e., $$a_{0} \approx GM/l_{0}^{2}$$, for astrophysical structures of mass M, and the deep-MOND regime is present in regions of space where the dimension is reduced to $$D \approx 2$$. For several fundamental spherically-symmetric structures, we compare MOND results, such as the empirical Radial Acceleration Relation (RAR), circular speed plots, and logarithmic plots of the observed radial acceleration $$g_{obs}$$ vs. the baryonic radial acceleration $$g_{bar}$$, with NFDG results. We show that our model is capable of reproducing these results using a variable local dimension $$D\left( w\right)$$, where $$w =r/l_{0}$$ is a dimensionless radial coordinate. At the moment, we are unable to derive explicitly this dimension function $$D\left( w\right)$$ from first principles, but it can be obtained empirically in each case from the general RAR. Additional work on the subject, including studies of axially-symmetric structures, detailed galactic rotation curves fitting, and a possible relativistic extension, will be needed to establish NFDG as a viable alternative model of gravity. (shrink)

Expected utility maximization problem is one of the most useful tools in mathematical finance, decision analysis and economics. Motivated by statistical model selection, via the principle of expected utility maximization, Friedman and Sandow (J Mach Learn Res 4:257–291, 2003a) considered the model performance question from the point of view of an investor who evaluates models based on the performance of the optimal strategies that the models suggest. They interpreted their performance measures in information theoretic terms and provided new generalizations of (...) Shannon entropy and Kullback–Leibler relative entropy and called them U-entropy and U-relative entropy. In this article, a utility-based criterion for independence of two random variables is defined. Then, Markov’s inequality for probabilities is extended from the U-entropy viewpoint. Moreover, a lower bound for the U-relative entropy is obtained. Finally, a link between conditional U-entropy and conditional Renyi entropy is derived. (shrink)

How is it possible that a thing singled out not exist? How is it possible that two things singled out be numerically identical? How is one to understand the relationship between, say, a quality of a thing and what this quality is? And how is one to understand the relation between this quality and the thing which happens to be thus qualified? Trying to answer these four questions involves investigation of the four senses of the verb "to be," or of (...) the concepts of existence, identity, essential and accidental predication. Butchvarov’s thesis is that these four questions admit of a common answer, that the cornerstone of this comprehensive theory is an answer to the second question, and that this crucial answer depends on making some such distinction as his between "objects" and "entities." The bare bones of his argument are these: We commonly make statements of the form "a is b" where "a" and "b" are used referringly. A "material identity" statement of this form may be true. If true, it is about one thing; yet what it is about appears to be distinct things. This distinctness is not a real distinction among existents, nor does it arise solely or primarily from features of language. Butchvarov’s account is based on a distinction "of reason" between objects and entities. An entity is an existent, a constituent of the world. An object is whatever can be singled out once, and only once, in perception or imagination or in "thought". Entities as such cannot be singled out, yet they may be recognized through applications of a conceptual apparatus to objects. A material identity statement, then, states that two objects are one entity. If true, it is both about two distinct objects and about the one entity which each is. When two objects are judged to be one entity, then indiscernibility is enforced. Seeming counterexamples to the indiscernibility of identicals are explained in terms of the distinction between objects and entities. Though some applications of the concept of identity are relative to sortal characteristics, others are not. The latter are prior to the former. These primary judgments constitute the backbone of "thought" and discourse. They are governed by impersonal, nonhuman "paradigms." There are entities, of course; and there are objects, though as objects none exists. Some objects are entities, some are not. The notion of existence, like the notion of identity in its material role, is then a principle of classification, a concept. Butchvarov examines nine objections to this claim, and elaborates his distinction between objects and entities. He concludes that identifiability, hence indefinite reidentifiability, is the logically sufficient condition of applicability of the concept of existence. A statement such as "Socrates is white" is a disguised conjunction, viz., "Socrates has this color, and this color is white." The second conjunct is an "essential" statement; it says of an object singled out that it is a certain entity; or, to allow for essences of nonexistent objects, it states what entity the object would be were it an entity. An essential statement is not a material identity statement, for only one of its terms is used referringly. The essence of an object is not a property of it, for it is what the object is or would be. Whereas logically prior consciousness of objects is intentional and non-conceptual, consciousness of entities is conceptual and nonintentional; it consists in recognizing that a thing can be identified by oneself or by others. What is accidentally white, say, cannot be a material substance or bare particular; therefore it is a "cluster" of qualities. The Resemblance Theory, according to which qualities are particulars, is not a coherent alternative to the Identity Theory; therefore the qualities an individual happens to have are themselves universals. The Bradleyan critique of ontological atomism is cogent; therefore an individual is a cluster of qualities each of which depends for its "formal identity" on its being together with the rest. An individual’s having qualities is then to be understood in terms of the necessary togetherness of the qualities constitutive of it. Since in addition each of these qualities is essentially a universal, and specific universals are contingently coinstantiated, the predication in question is properly regarded as accidental. The problem of identifying quality-clusters through space and time is discussed. (shrink)

A generalization of Ehrenfest''s urn model is suggested. This will allow usto treat a wide class of stochastic processes describing the changes ofmicroscopic objects. These processes are homogeneous Markov chains. Thegeneralization proposed is presented as an abstract conditional (relative)probability theory. The probability axioms of such a theory and some simpleadditional conditions, yield both transition probabilities and equilibriumdistributions. The resulting theory interpreted in terms of particles andsingle-particle states, leads to the usual formulae of quantum and classicalstatistical mechanics; in terms of (...) chromosomes and allelic types, it allowsthe deduction of many genetical models including the Ewens sampling formula;in terms of agents'' strategies, it gives a justification of the ``herdbehaviour'''' typical of a population of heterogeneous economic agents. (shrink)

Correct chromosome segregation in mitosis relies on chromosome biorientation, in which sister kinetochores attach to microtubules from opposite spindle poles prior to segregation. To establish biorientation, aberrant kinetochore–microtubule interactions must be resolved through the error correction process. During error correction, kinetochore–microtubule interactions are exchanged (swapped) if aberrant, but the exchange must stop when biorientation is established. In this article, we discuss recent findings in budding yeast, which have revealed fundamental molecular mechanisms promoting this “swap and stop” process for error correction. (...) Where relevant, we also compare the findings in budding yeast with mechanisms in higher eukaryotes. Evidence suggests that Aurora B kinase differentially regulates kinetochore attachments to the microtubule end and its lateral side and switches relative strength of the two kinetochore–microtubule attachment modes, which drives the exchange of kinetochore–microtubule interactions to resolve aberrant interactions. However, Aurora B kinase, recruited to centromeres and inner kinetochores, cannot reach its targets at kinetochore–microtubule interface when tension causes kinetochore stretching, which stops the kinetochore–microtubule exchange once biorientation is established. (shrink)

In this paper, we characterize the possible cofinalities of the least $\lambda $ -strongly compact cardinal. We show that, on the one hand, for any regular cardinal, $\delta $, that carries a $\lambda $ -complete uniform ultrafilter, it is consistent, relative to the existence of a supercompact cardinal above $\delta $, that the least $\lambda $ -strongly compact cardinal has cofinality $\delta $. On the other hand, provably the cofinality of the least $\lambda $ -strongly compact cardinal always carries (...) a $\lambda $ -complete uniform ultrafilter. (shrink)

This study presents findings from an ontological and contextual determination of the concept of dignity. The study had a caritative and caring science perspective and a hermeneutical design. The aim of this study was to increase caring science knowledge of dignity and to gain a determination of dignity as a concept. Eriksson’s model for conceptual determination is made up of five part-studies. The ontological and contextual determination indicates that dignity can be understood as absolute dignity, the spiritual dimension characterized by (...) responsibility, freedom, duty, and service, and relative dignity, characterized by the bodily, external aesthetic dimension and the psychical, inner ethical dimension. Dignity exists in human beings both as absolute and relative dignity. (shrink)

With concerns regarding climate change rising, companies and policy makers seek to understand the precursors to environmentally-friendly consumer choice. Decision modes are the qualitatively different psychological processes employed to arrive at decisions. Across six studies, the present project establishes (a) which decision modes are employed by consumers to decide between electricity plans that differ in environmental impact, and (b) how employed decision modes affect those choices. We demonstrate that consumers are most likely to use Calculation Modes when facing such choices. (...) Importantly, we find that Affect or Role Modes promote more environmentally-friendly choices, while Calculation Modes decrease environmentally-friendly choices. Experimentally promoting use of a Role Mode over a Calculation Mode increases selection of environmentally-friendly alternatives, and the relative degree of employing the Role Mode mediates this effect. Our findings provide insight into how decision mode usage can alter environmental decisions, and suggest mechanisms and tools for marketers and policy makers to influence consumer choice. (shrink)

The brain adapts to changes that take place in the body. Deprivation of input results in size reduction of cortical representations, whereas an increase in input results in an increase of representational space. Amputation forms one of the most dramatic disturbances of the integrity of the body. The brain adapts in many ways to this breakdown of the afferent–efferent equilibrium. However, almost all studies focus on the sensorimotor consequences. It is not known whether adaptation takes place also at other “levels” (...) in the system. The present study addresses the question whether amputees dream about their intact body, as before the amputation, or about the body after the amputation and whether the dream content was a function of time since the amputation and type of amputation. The results show that the majority of the dreamers reported dreams about their intact body although the mean time that elapsed since the amputation was twelve years. There is no clear relation with the type of amputation. The results give modest evidence for the existence of a basic neural representation of the body that is, at least, partly genetically determined and by this relatively insensitive for changes in the sensory input. (shrink)

Background Informed consent confers upon participants the right to decline or accept participation in a study in equal measure. Consent declines can be used as a potential metric to assess the adequacy of the informed consent process. Limited literature is available on the reporting of consent declines in Clinical Research. We evaluated randomized controlled trials published in three high-impact factor journals for consent declines to assess the extent of exertion of autonomy by research participants. Methods CONSORT flow charts in RCTs (...) published in New England Journal of Medicine, The Lancet and Journal of the American Medical Association between 2012 and 2015 were evaluated. The total and per journal proportion of RCTs reporting consent declines was calculated. Percentage of consent declines was also compared based on number of centers and type of setting. Between-groups analysis was done using Chi Square, Chi Square for trend and a Crude odds ratio [95% C.I] were calculated. Results Only 3.7% of the published articles were RCTs. Of the 1103 RCTs, only 532 reported consent declines. JAMA had the highest RCTs reporting consent declines, the Lancet [129,150/781,924, 16.5%] had the most participants declining consent. Difference was significant using Chi square for linear trend [ p < 0.00001]. Consent decline rate was higher in developed countries relative to developing countries [cOR: 2.27, p < 0.000001] and in single centric versus multicentric studies [cOR : 3.63, p < 0.0000001]. Conclusion Both authors and journal editors need to ensure better reporting of consent declines. (shrink)

Using 2003 Asian Barometer Survey study data, this paper examines the economic voting model in the 2002 presidential election in South Korea. The core emphasis of the paper is on an investigation of the relative effects of different dimensions/scopes of economic evaluations on voting behavior, namely whether one form of assessment (e.g., pocketbook vs. sociotropic) can have similar consequences for electoral participation as others. The findings indicate that the overall economy is salient for Koreans to shape their political choices. (...) In other words, voting behavior in Korea depends on how she or he thinks the national economy has been for the past five years. Also found is that voters’ perceptions of their own personal financial situations did not matter much as a predictor of voter choice. (shrink)

The current research investigated the role of gratitude in economic decisions about offers that vary in fairness yet benefit both parties if accepted. Participants completed a trait/dispositional gratitude measure and then were randomly assigned to recall either an event that made them feel grateful or the events of a typical day. After the gratitude induction task, participants played the ultimatum game, deciding whether to accept or reject fair offers and unfair offers from different proposers. Results showed that trait gratitude was (...) positively correlated with respondents’ acceptance of unfair offers. However, experimentally induced momentary gratitude did not influence acceptance of unfair offers. The trait or disposition to be grateful involves the enduring capacity across different types of situations and benefactors to see the good that is present, even when that benefit is small. Accordingly, dispositional gratitude – but not momentarily induced gratitude – was associated with a greater propensity to accept even the small benefits within unfair offers which otherwise pose barriers to making the effective economic decision of accepting offers regardless of their relative size. (shrink)

A cornerstone of physics, Maxwell‘s theory of electromagnetism, apparently contains a fatal flaw. The standard expressions for the electromagnetic field energy and the self-mass of an electron of finite extension do not obey Einstein‘s famous equation, \, but instead fulfill this relation with a factor 4/3 on the left-hand side. Furthermore, the energy and momentum of the electromagnetic field associated with the charge fail to transform as a four-vector. Many famous physicists have contributed to the debate of this so-called 4/3-problem (...) without arriving at a complete solution. It has generally been assumed that, as originally suggested by Poincaré, the problems are connected to the question of stability of the charge distribution, and that relativistic equivalence between energy and self-mass can only be restored by inclusion of stabilizing forces. Alternative solutions to the problems have also been proposed. Nearly a century ago Fermi suggested a covariant definition of the electromagnetic energy and momentum, and sixty years later Kalckar et al. argued that the 4/3 problem is caused by omission of a relativistic correction in the standard evaluation of the self-force from Coulomb self-interaction. However, the relation between these suggestions has not been clear. We show that the relativistic correction implies that the mechanical momentum of an accelerated rigid body must be defined as the sum of the momenta of its parts for fixed time in the momentary rest frame of the body. For the total momentum of particles and field to be conserved, the total energy–momentum tensor must be divergence free, and this then requires that the momentum of the associated electromagnetic field be defined in the same way, consistent with the suggestion by Fermi. This comprehensive solution of the 4/3-problem demonstrates that there is no conflict of Maxwell‘s theory with special relativity and the questions of equivalence of electromagnetic energy and self-mass and of stability of a classical charge distribution are independent. In appendices we discuss the relations of our treatment with Fermi‘s seminal paper and with a classic paper by Dirac where he evaluated the damping self-force on a point electron from transport of energy and momentum in the electromagnetic field. (shrink)

The essence of temporal universe creation is that any analytical solution has to comply with the boundary condition of our universe; dimensionality and causality constraints. The essence of this book is to show that everything has a price within our temporal (t > 0) universe; energy and time.

An analysis of some of the applications of Clifford space relativity to the physics behind the modified black hole entropy-area relations, rainbow metrics, generalized dispersion and minimal length stringy uncertainty relations is presented.

An extended scale relativity theory, actively developed by one of the authors, incorporates Nottale's scale relativity principle where the Planck scale is the minimum impassible invariant scale in Nature, and the use of polyvector-valued coordinates in C-spaces (Clifford manifolds) where all lengths, areas, volumes⋅ are treated on equal footing. We study the generalization of the ordinary point-particle quantum mechanical oscillator to the p-loop (a closed p-brane) case in C-spaces. Its solution exhibits some novel features: an emergence of two explicit scales (...) delineating the asymptotic regimes (Planck scale region and a smooth region of a quantum point oscillator). In the most interesting Planck scale regime, the solution recovers in an elementary fashion some basic relations of string theory (including string tension quantization and string uncertainty relation). It is shown that the degeneracy of the first collective excited state of the p-loop oscillator yields not only the well-known Bekenstein–Hawking area-entropy linear relation but also the logarithmic corrections therein. In addition we obtain for any number of dimensions the Hawking temperature, the Schwarschild radius, and the inequalities governing the area of a black hole formed in a fusion of two black holes. One of the interesting results is a demonstration that the evaporation of a black hole is limited by the upper bound on its temperature, the Planck temperature. (shrink)

Traditional diversity measures such as the Shannon entropy are generally computed from the species' relative abundance vector of a given community to the exclusion of species' absolute abundances. In this paper, I first mention some examples where the total information content associated with a given community may be more adequate than Shannon's average information content for a better understanding of ecosystem functioning. Next, I propose a parametric measure of statistical information that contains both Shannon's entropy and total (...) information content as special cases of this more general function. (shrink)

‘First. That on October 23, in the city of New York, your relator was arrested by divers persons claiming to be acting by authority of the government of the United States, and was by said persons conveyed to the United States immigration station at Ellis island, in the harbor of New York, and is now there imprisoned by the commissioner of immigration of the port of New York.

The principle of maximum entropy is a general method to assign values to probability distributions on the basis of partial information. This principle, introduced by Jaynes in 1957, forms an extension of the classical principle of insufficient reason. It has been further generalized, both in mathematical formulation and in intended scope, into the principle of maximum relative entropy or of minimum information. It has been claimed that these principles are singled out as unique methods of statistical inference (...) that agree with certain compelling consistency requirements. This paper reviews these consistency arguments and the surrounding controversy. It is shown that the uniqueness proofs are flawed, or rest on unreasonably strong assumptions. A more general class of inference rules, maximizing the so-called Re[acute ]nyi entropies, is exhibited which also fulfill the reasonable part of the consistency assumptions. (shrink)

We present a theory of cooperative-competitive intelligence (CCI), its measures, research program, and applications that stem from it. Within the framework of this theory, satisficing sub-optimal behavior is any behavior that does not promote a decrease in the prospective control of the functional action diversity/unpredictability (D/U) potential of the agent or team. This potential is defined as the entropy measure in multiple, context-dependent dimensions. We define the satisficing interval of behaviors as CCI. In order to manifest itself at individual (...) or team level, this capacity harnesses properties such as degeneracy, pleiotropy (pluri-potentiality), synergies, and metastability. Intelligence is embodied because intelligent behavior is deeply dependent on body functionalities, defined as entropy measures. We base our theory on three principles: (a) relativity of functional entropy/ information in agent (team)-environment systems, (b) tendency toward the satisficing level of D/U potential, and (c) tendency toward the non-decreasing D/U potential. The conjunction of these three principles provides existence of sub-optimal behaviors associated with CCI. First, we deal with the problem of how to reduce multidimensional behavior to a concept that accounts for the vast set of scenarios in which CCI is manifested. Secondly, we define and discuss the three interacting principles that underpin CCI behavior as well as providing an outline for a future CCI research program supported by agent￾based modeling and empirical research. Finally, we provide some preliminary practical issues that stem from the theory. (shrink)

It is a fundamental cornerstone of thermodynamics that entropy (SU,V\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S_{U,V}$$\end{document}) increases in spontaneous processes in isolated systems (often called closed or thermally closed systems when the transfer of energy as work is considered to be negligible) and achieves a maximum when the system reaches equilibrium. But with a different sign convention entropy could just as well be said to decrease to a minimum in spontaneous constant U, V processes. It (...) would then change in the same direction as the thermodynamic potentials in spontaneous processes. This article discusses but does not advocate such a change. (shrink)

Pour étendre la notion d'entropie, l'auteur tente de dégager la signification de la “probabilité relative” w de Boltzmann dans sa formule S = k.log.w. Celui-ci introduit implicitement une partition d'un ensemble E de molécules en classes d'équivalence, les divers états macroscopiques du gaz; w est le rapport de la probabilité de l'état dont on cherche à définir l'entropie à celle de l'état le plus improbable.L'auteur propose de généraliser le concept toutes les fois ob sur un ensemble probabilisable E il (...) sera possible de faire une partition.La “complexité d'une structure” peut être définie par le nombre d'aspects différents que peut prendre le graphe sous-jacent à celle-ci. Alors toute stricture a une probabilité d'occurrence, et l'on peut y définir une G-entropie.Appliquant ensuite ce concept à la théorie de l'information de Shannon, l'auteur montre que la quantité d'information apportée par un message est différente de la G-entropie, mais que les deux grandeurs y prennent fortuitement la même valeur. Le concept permet également d'introduire une information liée au message, une autre au “code”, et une information totale.Le concept d'émergence permet ensuite de comprendre la raison pour laquelle celle-ci s'accompagne d'une augmentation de G-neguentropie.L'entropie est considérée depuis Boltzmann comme une borne mesure du désordre d'un gaz, d'où son intérêt en morphogénèse, en théorie des systèmes, et de l'information. Cependant son application directe pose des problèmes, et il parait préférable de tenter auparavant de généraliser le concept en le randant plus abstrait. La première difficulté à laquelle on se heurte alors est l'interprétation du nombre w de la formule de Boltzmann. (shrink)

In a series of recent papers, Randall and Foulis have developed a generalized theory of probability (operational statistics) which is based on the notion of a physical operation. They have shown that the quantum logic description of quantum mechanics can be naturally imbedded into this generalized theory of probability. In this paper we shall investigate the role of entropy (in the sense of Shannon's theory of information) in operational statistics. We shall find that there are several related entropy (...) concepts in operational statistics. We shall examine the relationships between these different entropy concepts and examine their implications for the foundations of quantum theory. We shall also examine the extension of the Jaynes inference scheme to the operational statistics formalism, and apply the latter to the case of quantum statistical mechanics. (shrink)