Development of Econophysics: A Biased Account and Perspective from Kolkata

Kinetic exchange income distribution models with saving propensities: inequality indices and self-organized poverty level

We report the numerical results for the steady-state income or wealth distribution [Formula: see text] and the resulting inequality measures (Gini [Formula: see text] and Kolkata [Formula: see text] indices) in the kinetic exchange models of market dynamics. We study the variations of [Formula: see text] and of the indices [Formula: see text] and [Formula: see text] with the saving propensity [Formula: see text] of the agents, with two different kinds of trade (kinetic exchange) dynamics. In the first case, the exchange occurs between randomly chosen pairs of agents and in the next, one of the agents in the chosen pair is the poorest of all and the other agent is randomly picked up from the rest of the population (where, in the steady state, a self-organized poverty level or SOPL appears). These studies have also been made for two different kinds of saving behaviours. One, where each agent has the same value of [Formula: see text] (constant over time) and the other where [Formula: see text] for each agent can take two values (0 and 1), changing randomly over a fraction of time [Formula: see text] of choosing [Formula: see text]. We find that the inequality decreases with increasing savings ([Formula: see text]); inequality indices ([Formula: see text] and [Formula: see text]) decrease and SOPL increases with increasing [Formula: see text], indicating possible applications in economic policy making. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.

Stochastic Learning in Kolkata Paise Restaurant Problem: Classical and Quantum Strategies

We review the results for stochastic learning strategies, both classical (one-shot and iterative) and quantum (one-shot only), for optimizing the available many-choice resources among a large number of competing agents, developed over the last decade in the context of the Kolkata Paise Restaurant (KPR) Problem. Apart from few rigorous and approximate analytical results, both for classical and quantum strategies, most of the interesting results on the phase transition behavior (obtained so far for the classical model) uses classical Monte Carlo simulations. All these including the applications to computer science [job or resource allotments in Internet-of-Things (IoT)], transport engineering (online vehicle hire problems), operation research (optimizing efforts for delegated search problem, efficient solution of Traveling Salesman problem) will be discussed.

Social inequality analysis of fiber bundle model statistics and prediction of materials failure

Inequalities are abundant in a society with a number of agents competing for a limited amount of resources. Statistics on such social inequalities are usually represented by the Lorenz function L(p), where p fraction of the population possesses L(p) fraction of the total wealth, when the population is arranged in ascending order of their wealth. Similarly, in scientometrics, such inequalities can be represented by a plot of the citation count versus the respective number of papers by a scientist, again arranged in ascending order of their citation counts. Quantitatively, these inequalities are captured by the corresponding inequality indices, namely, the Kolkata k and the Hirsch h indices, given by the fixed points of these nonlinear (Lorenz and citation) functions. In statistical physics of criticality, the fixed points of the renormalization group generator functions are studied in their self-similar limit, where their (fractal) structure converges to a unique form (macroscopic in size and lone). The statistical indices in social science, however, correspond to the fixed points where the values of the generator function (wealth or citation sizes) are commensurately abundant in fractions or numbers (of persons or papers). It has already been shown that under extreme competitions in markets or at universities, the k index approaches a universal limiting value, as the dynamics of competition progresses. We introduce and study these indices for the inequalities of (prefailure) avalanches, given by their nonlinear size distributions in fiber bundle models of nonbrittle materials. We show how prior knowledge of the terminal and (almost) universal value of the k index for a wide range of disorder parameters can help in predicting an imminent catastrophic breakdown in the model. This observation is also complemented by noting a similar (but not identical) behavior of the Hirsch index (h), redefined for such avalanche statistics.

Entropy and Wealth

While entropy was introduced in the second half of the 19th century in the international vocabulary as a scientific term, in the 20th century it became common in colloquial use. Popular imagination has loaded “entropy” with almost every negative quality in the universe, in life and in society, with a dominant meaning of disorder and disorganization. Exploring the history of the term and many different approaches to it, we show that entropy has a universal stochastic definition, which is not disorder. Hence, we contend that entropy should be used as a mathematical (stochastic) concept as rigorously as possible, free of metaphoric meanings. The accompanying principle of maximum entropy, which lies behind the Second Law, gives explanatory and inferential power to the concept, and promotes entropy as the mother of creativity and evolution. As the social sciences are often contaminated by subjectivity and ideological influences, we try to explore whether maximum entropy, applied to the distribution of a wealth-related variable, namely annual income, can give an objective description. Using publicly available income data, we show that income distribution is consistent with the principle of maximum entropy. The increase in entropy is associated to increases in society’s wealth, yet a standardized form of entropy can be used to quantify inequality. Historically, technology has played a major role in the development of and increase in the entropy of income. Such findings are contrary to the theory of ecological economics and other theories that use the term entropy in a Malthusian perspective.