Transactional Interpretation for the Principle of Minimum Fisher Information

The principle of minimum Fisher information states that in the set of acceptable probability distributions characterizing the given system, it is best done by the one that minimizes the corresponding Fisher information. This principle can be applied to transaction processes, the dynamics of which can be interpreted as the market tendency to minimize the information revealed about itself. More information involves higher costs (information is physical). The starting point for our considerations is a description of the market derived from the assumption of minimum Fisher information for a strategy with a fixed financial risk. Strategies of this type that minimize Fisher information overlap with the well-known eigenstates of a the quantum harmonic oscillator. The analytical extension of this field of strategy to the complex vector space (traditional for quantum mechanics) suggests the study of the interference of the oscillator eigenstates in terms of their minimization of Fisher information. It is revealed that the minimum value of Fisher information of the superposition of the two strategies being the ground state and the second excited state of the oscillator, has Fisher information less than the ground state of the oscillator. Similarly, less information is obtained for the system of strategies (the oscillator eigenstates) randomized by the Gibbs distribution. We distinguish two different views on the description of Fisher information. One of them, the classical, is based on the value of Fisher information. The second, we call it transactional, expresses Fisher information from the perspective of the constant risk of market strategies. The orders of the market strategies derived from these two descriptions are different. From a market standpoint, minimizing Fisher information is equivalent to minimizing risk.

Classical Partition Function for Non-Relativistic Gravity

We considered the canonical gravitational partition function Z associated to the classical Boltzmann–Gibbs (BG) distribution e−βHZ. It is popularly thought that it cannot be built up because the integral involved in constructing Z diverges at the origin. Contrariwise, it was shown in (Physica A 497 (2018) 310), by appeal to sophisticated mathematics developed in the second half of the last century, that this is not so. Z can indeed be computed by recourse to (A) the analytical extension treatments of Gradshteyn and Rizhik and Guelfand and Shilov, that permit tackling some divergent integrals and (B) the dimensional regularization approach. Only one special instance was discussed in the above reference. In this work, we obtain the classical partition function for Newton’s gravity in the four cases that immediately come to mind.

Impact value and sustainable, well-being centred service systems

Purpose This paper aims to develop impact value (IV), both theoretically and practically, to better account for the processes of value creation within complex service ecosystems. Design/methodology/approach This conceptual paper connects the complex systems nature of service ecosystems and the complexity of issues of sustainability and well-being to the need for a conceptual and analytical extension of value within service ecosystems. Findings This paper defines IV as enhancement or diminishment of the potential of stakeholders (beyond the service beneficiary), to transfer or transform resources in the future, based on direct and indirect involvement in the processes of value-in-exchange and value-in-use creation. Research limitations/implications This paper provides an initial exploration of the theoretical and practical extension of value through the IV concept. Practical implications Sustainable service ecosystems require actors to understand their role in the service process and account for the impact pathways of their value creation activities. This paper proposes a framework for developing sustainable strategies to account for IV. Originality/value This research expands service research’s core concept of value by integrating the complex systems nature of service ecosystems, sustainability and well-being. IV provides a means to address the systemic impact pathways of service and value creation processes and bridge idiosyncratic value-in-use and broader system viability concepts.

Aplicación del método de resumación de Borel en la ecuación diferencial de Euler

El propósito de este artículo es mostrar que a partir de la series divergentes se puede obtener información relevante que permite resolver algunos problemas, para lograr este cometido, inicialmente se hace una breve introducción a la teoría resurgente de Écalle, se establecen las definiciones básicas como: resumación de Borel, serie clase Gevrey1 e introducimos las herramientas necesarias, entre ellas la transformada de Borel y Laplace, además se hace un esquema de los pasos que se deben seguir para usar el método de resumación de Borel. Se muestra como ejemplo la ecuación diferencial de Euler, de la cual se halla una solución en forma de serie formal divergente. Siguiendo el esquema del método se debe calcular en primer lugar la transformada de Borel y asociar esta con una función que es analítica en un dominio, para así definir el dominio de la transformada de Laplace y obtener por extensión analítica las soluciones al problema inicial. Luego de este procedimiento las soluciones al problema inicial no deben estar dado por una serie divergente y en su lugar puede ser representado por integrales con caminos distintos, esto último puede permitir establecer relaciones entre las soluciones.. Palabras claves: resumación de Borel, ecuación diferencial de Euler, series divergentes. Abstract The purpose of this article is to show that from the divergent series it is possible to obtain relevant information that allows solving some problems, to achieve this task, initially a brief introduction to the resurgent theory of Écalle is made, the basic definitions are established such as: Borel summarization, Gevrey1 class series and we introduce the necessary tools, among them the Borel and Laplace transform, we also outline the steps that must be followed to use the Borel summarization method. Euler’s differential equation is shown as an example, of which a solution is found in the form of a divergent formal series. Following the scheme of the method, the Borel transform must first be calculated and associated with a function that is analytic in a domain, in order to define the domain of the Laplace transform and obtain by analytical extension the solutions to the initial problem. After this procedure, the solutions to the initial problem should not be given by a divergent series and instead can be represented by integrals with different paths, the latter can allow establishing relationships between the solutions. Keywords: Borel’s summary, Euler differential equation, series divergent.

A Review of the Classical Canonical Ensemble Treatment of Newton’s Gravitation

It is common lore that the canonical gravitational partition function Z associated with the classical Boltzmann-Gibbs (BG) exponential distribution cannot be built up because of mathematical pitfalls. The integral needed for writing up Z diverges. We review here how to avoid this pitfall and obtain a (classical) statistical mechanics of Newton’s gravitation. This is done using (1) the analytical extension treatment obtained of Gradshteyn and Rizhik and (2) the well known dimensional regularization technique.

Seeing relativity-I: Ray tracing in a Schwarzschild metric to explore the maximal analytic extension of the metric and making a proper rendering of the stars

We present an implementation of a ray tracing code in the Schwarzschild metric. We aim at building a numerical code with a correct implementation of both special (aberration, amplification and Doppler) and general (deflection of light, lensing and gravitational redshift) relativistic effects so as to simulate what an observer with arbitrary velocity would see near, or possibly within, the black hole. We also pay some specific attention to perform a satisfactory rendering of stars. Using this code, we then show several unexplored features of the maximal analytical extension of the metric. In particular, we study the aspect of the second asymptotic region of the metric as seen by an observer crossing the horizon. We also address several aspects related to the white hole region (i.e. past singularity) seen both from outside the black hole, inside the future horizon and inside the past horizon, which gives rise to the most counter-intuitive effects.