arXiv subjects
Publications and source records attributed to Ricardo Lopez-Ruiz.
In simulations of some economic gas-like models, the asymptotic regime shows an exponential wealth distribution, independently of the initial wealth distribution given to the system. The appearance of this statistical equilibrium for this type of gas-like models is explained in a rigorous analytical way.
Exponential distribution is ubiquitous in the framework of multi-agent systems. Usually, it appears as an equilibrium state in the asymptotic time evolution of statistical systems. It has been explained from very different perspectives. In statistical physics, it is obtained from the principle of maximum entropy. In the same context, it can also be derived without any consideration about information theory, only from geometrical arguments under the hypothesis of equiprobability in phase space. Also, several multi-agent economic models based on mappings, with random, deterministic or chaotic interactions, can give rise to the asymptotic appearance of the exponential wealth distribution. An alternative approach to this problem in the framework of iterations in the space of distributions has been recently presented. Concretely, the new iteration given by $ f_{n+1}(x) = \int\int_{u+v>x}{f_n(u)f_n(v)\over u+v} dudv.$. It is found that the exponential distribution is a stable fixed point of the former functional iteration equation. From this point of view, it is easily understood why the exponential wealth distribution (or by extension, other kind of distributions) is asymptotically obtained in different multi-agent economic models.
Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics offers models of markets as complex systems, that try to comprehend macro-, system-wide states of the economy from the interaction of many agents at micro-level. One of these models is the gas-like model for trading markets. This tries to predict money distributions in closed economies and quite simply, obtains the ones observed in real economies. However, it reveals technical hitches to explain the power law distribution, observed in individuals with high incomes. In this work, non linear dynamics is introduced in the gas-like model in way that an effort to overcome these flaws. A particular chaotic dynamics is used to break the pairing symmetry of agents $(i,j)\Leftrightarrow(j,i)$. The results demonstrate that a "chaotic gas-like model" can reproduce the Exponential and Power law distributions observed in real economies. Moreover, it controls the transition between them. This may give some insight of the micro-level causes that originate unfair distributions of money in a global society. Ultimately, the chaotic model makes obvious the inherent instability of asymmetric scenarios, where sinks of wealth appear and doom the market to extreme inequality.
A step by step procedure to derive analytically the exact dynamical evolution equations of the probability density functions (PDF) of well known kinetic wealth exchange economic models is shown. This technique gives a dynamical insight into the evolution of the PDF, e.g., allowing the calculation of its relaxation times. Their equilibrium PDFs can also be calculated by finding its stationary solutions. This gives as a result an integro-differential equation, which can be solved analytically in some cases and numerically in others. This should provide some guidance into the type of probability density functions that can be derived from particular economic agent exchange rules, or for that matter, any other kinetic model of gases with particular collision physics.
Exponential distribution is ubiquitous in the framework of multi-agent systems. An alternative approach with an economic motivation to derive the exponential distribution in the framework of iterations in the space of distributions is disclosed.
In this chapter, a statistical measure of complexity is introduced and some of its properties are discussed. Also, some straightforward applications are shown.
Nowadays the question `what is complexity?' is a challenge to be answered. This question is triggering a great quantity of works in the frontier of physics, biology, mathematics and computer science. Even more when this century has been told to be the century of Complexity. Although there seems to be no urgency to answer the above question, many different proposals that have been developed to this respect can be found in the literature. In this context, several articles concerning statistical complexity and stochastic processes are collected in this chapter.
Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics is offering models of markets as complex systems, such as the gas-like model, able to predict money distributions observed in real economies. However, this model reveals some technical hitches to explain the power law (Pareto) distribution, observed in individuals with high incomes. Here, non linear dynamics is introduced in the gas-like model. The results obtained demonstrate that a chaotic gas-like model can reproduce the two money distributions observed in real economies (Exponential and Pareto). Moreover, it is able to control the transition between them. This may give some insight of the micro-level causes that originate unfair distributions of money in a global society. Ultimately, the chaotic model makes obvious the inherent instability of asymmetric scenarios, where sinks of wealth appear in the market and doom it to complete inequality.
In this paper, we analyze the behavior of statistical complexity in several systems where two identical densities that travel in opposite direction cross each other. Besides the crossing between two Gaussian, rectangular and triangular densities studied in a previous work, we also investigate in detail the crossing between two exponential and two gamma distributions. For all these cases, the shape of the total density presenting an extreme value in complexity is found.
Two-dimensional maps can model interactions between populations. Despite their simplicity, these dynamical systems can show some complex situations, as multistability or fractal boundaries between basins that lead to remarkable pictures. Some of them are shown and explained here for three different 2D discrete models.
In this work, the proofs concerning the continuity of the disequilibrium, Shannon information and statistical complexity in the space of distributions are presented. Also, some results on the existence of Shannon information for continuous systems are given.
In this work, a shell model for metal clusters up to 220 valence electrons is used to obtain the fractional occupation probabilities of the electronic orbitals. Then, the calculation of a statistical measure of complexity and the Fisher-Shannon information is carried out. An increase of both magnitudes with the number of valence electrons is observed. The shell structure is reflected by the behavior of the statistical complexity. The magic numbers are indicated by the Fisher-Shannon information. So, as in the case of atomic nuclei, the study of statistical indicators also unveil the existence of magic numbers in metal clusters.
In this communication, the derivation of the Boltzmann-Gibbs and the Maxwellian distributions is presented from a geometrical point of view under the hypothesis of equiprobability. It is shown that both distributions can be obtained by working out the properties of the volume or the surface of the respective geometries delimited in phase space by an additive constraint. That is, the asymptotic equilibrium distributions in the thermodynamic limit are independent of considering open or closed homogeneous statistical systems.
In this work, we analyze the behavior of statistical complexity in several systems where two identical densities that travel in opposite direction cross each other. The crossing between two Gaussian, rectangular and triangular densities is studied in detail. For these three cases, the shape of the total density presenting an extreme value in complexity is found.
The calculation of a statistical measure of complexity and the Fisher-Shannon information in nuclei is carried out in this work. We use the nuclear shell model in order to obtain the fractional occupation probabilities of nuclear orbitals. The increasing of both magnitudes, the statistical complexity and the Fisher-Shannon information, with the number of nucleons is observed. The shell structure is reflected by the behavior of the statistical complexity. The magic numbers are revealed by the Fisher-Shannon information.
This paper considers the ideal gas-like model of trading markets, where each individual is identified as a gas molecule that interacts with others trading in elastic or money-conservative collisions. Traditionally this model introduces different rules of random selection and exchange between pair agents. Real economic transactions are complex but obviously non-random. Consequently, unlike this traditional model, this work implements chaotic elements in the evolution of an economic system. In particular, we use a chaotic signal that breaks the natural pairing symmetry $(i,j)\Leftrightarrow(j,i)$ of a random gas-like model. As a result of that, it is found that a chaotic market like this can reproduce the referenced wealth distributions observed in real economies (the Gamma, Exponential and Pareto distributions).
A naive model of many networked logistic maps with an excitation type coupling [Neural Networks, vol. 20, 102--108 (2007)], which is an extension of other low dimensional models, has been recently proposed to mimic the waking-sleeping bistability found in brain systems. Although the dynamics of large and complex aggregates of elementary components can not be understood nor extrapolated from the properties of a few components, some patterns of behavior could be conserved independently of the topology and of the number of coupled units. Following this insight, we have collected several of those systems where a few logistic maps are coupled under a similar mutual excitation scheme. The regions of bi- and multistability of these systems are sketched and reported.
In this work, the calculation of a statistical measure of complexity and the Fisher-Shannon information is performed for all the atoms in the periodic table. Non-relativistic and relativistic cases are considered. We follow the method suggested in [C.P. Panos, N.S. Nikolaidis, K. Ch. Chatzisavvas, C.C. Tsouros, arXiv:0812.3963v1] that uses the fractional occupation probabilities of electrons in atomic orbitals, instead of the continuous electronic wave functions. For the order of shell filling in the relativistic case, we take into account the effect due to electronic spin-orbit interaction. The increasing of both magnitudes, the statistical complexity and the Fisher-Shannon information, with the atomic number $Z$ is observed. The shell structure and the irregular shell filling is well displayed by the Fisher-Shannon information in the relativistic case.