Is econophysics a new discipline? The neopositivist argument

Econophysics is a new approach which applies various models and concepts associated with statistical physics to economic (and financial) phenomena. This field of research is a new step in the history and the evolution of Physics Sciences and the question about the disciplinary characteristics of this field must be asked. At first glance, it might appear that economics and econophysics share the same subject of research (that of analysis of economic reality). In this paper I will use neopositivism to show that econophysics is methodologically very different from economics and that it can be considered as a separate discipline. The neopositivist framework provides econophysics with some arguments for rejecting mainstream economics.     

Estimating income mobility using census data

This study uses the entropy method to overcome the problem with estimating income distribution dynamics in the absence of data that allow identifying and following up economic units over time. The axiomatic mobility approach (Shorrocks, 1976) [1] and the tools developed by Aebi et al. (1999) [2] were considered. This strategy assumes that income mobility between two time periods is governed by a first-order Markov process. In this context, the measurement of the dynamics of income distribution will be equivalent to fitting cell probabilities for contingency tables, where only marginal distributions are observed. Results suggest that Brazil has low intragenerational income mobility, indicating that its social framework is relatively rigid. In other words, the income class in which an individual is inserted will determine his/her future social position.     

An econophysics approach to analyse uncertainty in financial markets: an application to the Portuguese stock market

In recent years there has been a closer interrelationship between several scientific areas trying to obtain a more realistic and rich explanation of the natural and social phenomena. Among these it should be emphasized the increasing interrelationship between physics and financial theory. In this field the analysis of uncertainty, which is crucial in financial analysis, can be made using measures of physics statistics and information theory, namely the Shannon entropy. One advantage of this approach is that the entropy is a more general measure than the variance, since it accounts for higher order moments of a probability distribution function. An empirical application was made using data collected from the Portuguese Stock Market.     

Economic Cycles of Carnot Type

Originally, the Carnot cycle was a theoretical thermodynamic cycle that provided an upper limit on the efficiency that any classical thermodynamic engine can achieve during the conversion of heat into work, or conversely, the efficiency of a refrigeration system in creating a temperature difference by the application of work to the system. The first aim of this paper is to introduce and study the economic Carnot cycles concerning Roegenian economics, using our thermodynamic–economic dictionary. These cycles are described in both a Q−P diagram and a E−I diagram. An economic Carnot cycle has a maximum efficiency for a reversible economic “engine”. Three problems together with their solutions clarify the meaning of the economic Carnot cycle, in our context. Then we transform the ideal gas theory into the ideal income theory. The second aim is to analyze the economic Van der Waals equation, showing that the diffeomorphic-invariant information about the Van der Waals surface can be obtained by examining a cuspidal potential.     

Examining the Research on Business Information-Entropy Correlation in the Accounting Process of Organizations

Open business organizations, where information flows, is shared, and exchanged, are more prepared to adapt and survive chaos, uncertainty, and entropy, so they will be more predisposed to change management. The aim of this study is to analyze research trends at the international level on business information–entropy correlation in the accounting process of organizations. Mathematical and statistical techniques were applied to 980 articles during the period 1974–2020, obtaining results on the scientific productivity of the driving agents of this topic: authors, research institutions, countries/territories, and journals. Five lines of research were identified during the period analyzed, which mainly study information theory, maximum entropy, information entropy, decision-making, and enthalpy. Future research should focus on analyzing the evolution of this topic, which forms new thematic axes related to bitcoin market efficiency, business hierarchy information, business model evaluation systems, catastrophic economic collapse, corporate diversification, CSR reports affecting accounting conservatism, economic income accounting, and information loss. Currently, the research presents an upward trend, which allows a growing interest in the subject to be deduced in the academic and scientific community worldwide.     

Recent progress in econophysics: Chaos,leverage, and business cycles as revealed by agent-based modeling and human experiments

Agent-based modeling and controlled human experiments serve as two fundamental research methods in the field of econophysics. Agent-based modeling has been in development for over 20 years, but how to design virtual agents with high levels of human-like “intelligence” remains a challenge. On the other hand, experimental econophysics is an emerging field; however, there is a lack of experience and paradigms related to the field. Here, we review some of the most recent research results obtained through the use of these two methods concerning financial problems such as chaos, leverage, and business cycles. We also review the principles behind assessments of agents’ intelligence levels, and some relevant designs for human experiments. The main theme of this review is to show that by combining theory, agent-based modeling, and controlled human experiments, one can garner more reliable and credible results on account of a better verification of theory; accordingly, this way, a wider range of economic and financial problems and phenomena can be studied.     

Entropy and Entropic Forces to Model Biological Fluids

Living cells are complex systems characterized by fluids crowded by hundreds of different elements, including, in particular, a high density of polymers. They are an excellent and challenging laboratory to study exotic emerging physical phenomena, where entropic forces emerge from the organization processes of many-body interactions. The competition between microscopic and entropic forces may generate complex behaviors, such as phase transitions, which living cells may use to accomplish their functions. In the era of big data, where biological information abounds, but general principles and precise understanding of the microscopic interactions is scarce, entropy methods may offer significant information. In this work, we developed a model where a complex thermodynamic equilibrium resulted from the competition between an effective electrostatic short-range interaction and the entropic forces emerging in a fluid crowded by different sized polymers. The target audience for this article are interdisciplinary researchers in complex systems, particularly in thermodynamics and biophysics modeling.     

On the efficiency of sovereign bond markets

The existence of memory in financial time series has been extensively studied for several stock markets around the world by means of different approaches. However, fixed income markets, i.e. those where corporate and sovereign bonds are traded, have been much less studied. We believe that, given the relevance of these markets, not only from the investors’, but also from the issuers’ point of view (government and firms), it is necessary to fill this gap in the literature. In this paper, we study the sovereign market efficiency of thirty bond indices of both developed and emerging countries, using an innovative statistical tool in the financial literature: the complexity-entropy causality plane. This representation space allows us to establish an efficiency ranking of different markets and distinguish different bond market dynamics. We conclude that the classification derived from the complexity-entropy causality plane is consistent with the qualifications assigned by major rating companies to the sovereign instruments. Additionally, we find a correlation between permutation entropy, economic development and market size that could be of interest for policy makers and investors.     

An almost linear stochastic map related to the particle system models of social sciences

We propose a stochastic map model of economic dynamics. In the past decade, an array of observations in economics has been investigated in the econophysics literature, a major example being the universal features of inequality in terms of income and wealth. Another area of enquiry is the formation of opinion in a society. The model proposed attempts to produce positively skewed distributions and power law distributions as has been observed in the real data of income and wealth. Also, it shows a non-trivial phase transition in the opinion of a society (opinion formation). A number of physical models also generate similar results. In particular, kinetic exchange models have been successful especially in this regard. Therefore, we compare the results obtained from these two approaches and discuss a number of new features and drawbacks of this model.     

Coherence and Entropy of Credit Cycles across the Euro Area Candidate Countries

The pattern of financial cycles in the European Union has direct impacts on financial stability and economic sustainability in view of adoption of the euro. The purpose of the article is to identify the degree of coherence of credit cycles in the countries potentially seeking to adopt the euro with the credit cycle inside the Eurozone. We first estimate the credit cycles in the selected countries and in the euro area (at the aggregate level) and filter the series with the Hodrick–Prescott filter for the period 1999Q1–2020Q4. Based on these values, we compute the indicators that define the credit cycle similarity and synchronicity in the selected countries and a set of entropy measures (block entropy, entropy rate, Bayesian entropy) to show the high degree of heterogeneity, noting that the manifestation of the global financial crisis has changed the credit cycle patterns in some countries. Our novel approach provides analytical tools to cope with euro adoption decisions, showing how the coherence of credit cycles can be increased among European countries and how the national macroprudential policies can be better coordinated, especially in light of changes caused by the pandemic crisis.     

Stochastic Order and Generalized Weighted Mean Invariance

In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.     

Stokes integral of economic growth: Calculus and the Solow model

Economic growth depends on capital and labor and two-dimensional calculus has been applied to economic theory. This leads to Riemann and Stokes integrals and to the first and second laws of production and growth. The mathematical structure is the same as in thermodynamics, economic properties may be related to physical terms: capital to energy, production to physical work, GDP per capita to temperature, production function to entropy. This is called econophysics. Production, trade and banking may be compared to motors, heat pumps or refrigerators. The Carnot process of the first law creates two levels in each system: cold and hot in physics; buyer and seller, investor and saver, rich and poor in economics. The efficiency rises with the income difference of rich and poor. The results of econophysics are compared to neoclassical theory.     

重离子核反应中丰中子余核产额的标度规律

在重离子碰撞（HICs）的实验数据和动力学模拟的反应中发现了丰中子余核产额的标度现象。在这种标度现象中,两个同位旋不同的炮弹碎裂反应产生的余核中,不同中子丰度差的余核的信息熵不确定度的差具有一致的分布。利用反对称化分子动力学模型（AMD）模拟并联合退激发模型（GEMINI）模拟了140 AMeV 58,64Ni+9Be碰撞体系中余核的产额,并展示了实验测量的余核已经理论模拟得到的余核的标度现象。由于信息熵方法对反应系统是否处于平衡状态没有要求,不仅可以用于处于平衡态系统的核物质研究,也可以用于动力学变化过程中的核物质性质研究。信息熵方法将为HICs中的核物质演化研究提供新的理论分析方法。A scaling phenomena has been discovered for fragments produced in heavy-ion collisions both in the measured experiments and in the simulated reactions by transport model. In this scaling phenomena, the information entropy uncertainty difference between isobars with different neutron-excess has a uniform distribution between two reactions. The simulated reactions of 140 AMeV 58,64Ni+9Be by using the asymmetric molecular dynamics(AMD) model plus the sequential decay code GEMINI are analyzed to show the scaling phenomena of fragments. Since the application of information entropy theory does not require the system to be in equilibrium, it can be used both in the analysis of transport model and thermodynamics models. The advantage of the information entropy theory provides a new method to study the dynamical evolution of nuclear matter inheavy-ion collisions.     

Long memory and volatility clustering: Is the empirical evidence consistent across stock markets?

Long memory and volatility clustering are two stylized facts frequently related to financial markets. Traditionally, these phenomena have been studied based on conditionally heteroscedastic models like ARCH, GARCH, IGARCH and FIGARCH, inter alia. One advantage of these models is their ability to capture nonlinear dynamics. Another interesting manner to study the volatility phenomenon is by using measures based on the concept of entropy. In this paper we investigate the long memory and volatility clustering for the SP 500, NASDAQ 100 and Stoxx 50 indexes in order to compare the US and European Markets. Additionally, we compare the results from conditionally heteroscedastic models with those from the entropy measures. In the latter, we examine Shannon entropy, Renyi entropy and Tsallis entropy. The results corroborate the previous evidence of nonlinear dynamics in the time series considered.     

Efficient Markets and Contingent Claims Valuation: An Information Theoretic Approach

This research article shows how the pricing of derivative securities can be seen from the context of stochastic optimal control theory and information theory. The financial market is seen as an information processing system, which optimizes an information functional. An optimization problem is constructed, for which the linearized Hamilton–Jacobi–Bellman equation is the Black–Scholes pricing equation for financial derivatives. The model suggests that one can define a reasonable Hamiltonian for the financial market, which results in an optimal transport equation for the market drift. It is shown that in such a framework, which supports Black–Scholes pricing, the market drift obeys a backwards Burgers equation and that the market reaches a thermodynamical equilibrium, which minimizes the free energy and maximizes entropy.     

Pattern formation,social forces,and diffusion instability in games with success-driven motion

A local agglomeration of cooperators can support the survival or spreading of cooperation, even when cooperation is predicted to die out according to the replicator equation, which is often used in evolutionary game theory to study the spreading and disappearance of strategies. In this paper, it is shown that success-driven motion can trigger such local agglomeration and may, therefore, be used to supplement other mechanisms supporting cooperation, like reputation or punishment. Success-driven motion is formulated here as a function of the game-theoretical payoffs. It can change the outcome and dynamics of spatial games dramatically, in particular as it causes attractive or repulsive interaction forces. These forces act when the spatial distributions of strategies are inhomogeneous. However, even when starting with homogeneous initial conditions, small perturbations can trigger large inhomogeneities by a pattern-formation instability, when certain conditions are fulfilled. Here, these instability conditions are studied for the prisoner’s dilemma and the snowdrift game. Furthermore, it is demonstrated that asymmetrical diffusion can drive social, economic, and biological systems into the unstable regime, if these would be stable without diffusion.     

Entropy and equilibrium state of free market models

Many recent models of trade dynamics use the simple idea of wealth exchanges among economic agents in order to obtain a stable or equilibrium distribution of wealth among the agents. In particular, a plain analogy compares the wealth in a society with the energy in a physical system, and the trade between agents to the energy exchange between molecules during collisions. In physical systems, the energy exchange among molecules leads to a state of equipartition of the energy and to an equilibrium situation where the entropy is a maximum. On the other hand, in a large class of exchange models, the system converges to a very unequal condensed state, where one or a few agents concentrate all the wealth of the society while the wide majority of agents shares zero or almost zero fraction of the wealth. So, in those economic systems a minimum entropy state is attained. We propose here an analytical model where we investigate the effects of a particular class of economic exchanges that minimize the entropy. By solving the model we discuss the conditions that can drive the system to a state of minimum entropy, as well as the mechanisms to recover a kind of equipartition of wealth.     

Entropy Optimization,Maxwell–Boltzmann,and Rayleigh Distributions

In physics, communication theory, engineering, statistics, and other areas, one of the methods of deriving distributions is the optimization of an appropriate measure of entropy under relevant constraints. In this paper, it is shown that by optimizing a measure of entropy introduced by the second author, one can derive densities of univariate, multivariate, and matrix-variate distributions in the real, as well as complex, domain. Several such scalar, multivariate, and matrix-variate distributions are derived. These include multivariate and matrix-variate Maxwell–Boltzmann and Rayleigh densities in the real and complex domains, multivariate Student-t, Cauchy, matrix-variate type-1 beta, type-2 beta, and gamma densities and their generalizations.