arXiv subjects

Suchismita Banerjee

Publications and source records attributed to Suchismita Banerjee.

15 recordsLinked to original sources

arXiv2026

Relations Among Different Inequality Measures in Complex Systems: From Kinetic Exchange to Earthquake Models

We present a numerical study of several inequality measures across two kinetic wealth exchange models with extreme inequality features (namely the Banerjee model, and the Chakraborti or Yard Sale model) and two earthquake simulating models (namely the Chakrabarti Stinchcombe two fractal overlap model and the nonlinear dynamical Burridge Knopoff model). For each model we compute numerically the Lorenz function for the respective models wealth, overlap magnitude or avalanche distributions. We then estimate the variations of Gini (g), Pietra (p) and Kolkata (k) indices in these models with systematic variations of saving propensity (for the two wealth exchange models), with systematic variations of generation or block numbers (for the two earthquake simulating models). We find that for appropriate values of the respective model parameters, the inequality indices g and k in corresponding the distributions (of wealth or avalanche) show quantitatively similar behavior, namely g equal to k nearly equal to 0.86, which was identified earlier to correspond to the precursor point of criticality in self organized critical models (k equal to 0.80 corresponds to that for Pareto 80/20 law). The values of p/(2k-1) in all these (wealth exchange and earthquake) models remain a little above unity, as was predicted theoretically. These observations for the inequality indices g, k and p across the socio economic and geophysical models indicate the presence of unifying subtle features in the statistics of such disparate dynamical systems.

physics.soc-ph↗

arXiv2026

Exploring the impact of multi-agent wealth exchange model on inequality reduction

Binary kinetic exchange models, where money is shuffled between two agents at a time, reproduce the Boltzmann Gibbs exponential wealth distribution but cannot address the multi party trades common in real markets. We generalize the exchange rule to simultaneous interactions among more than two agents in a closed economical system. We observe, as number of agents grow, the stationary wealth distribution evolves smoothly from an exponential to an almost uniform distribution. Inequality metrics (Gini and k index) has been found to fall monotonically with the increase in agents number. Compared with binary models that rely on saving propensities, which is also known to reduce inequality, we find the multi agent interaction show a completely different behavior of inequality reduction.

physics.soc-ph↗

arXiv2026

Universal Features in Atmospheric Particulate Matter Dynamics

We study statistical properties of atmospheric particulate matter fluctuations using six years of daily PM2.5 concentration data from fifty-four Indian cities. Despite diverse urban settings and heterogeneous climatic conditions, we find that the fluctuations show strikingly universal behaviour in both the distributional properties and temporal dynamics. After removing slow trends and seasonal components, the rescaled probability density functions of the residual fluctuations collapse onto a single curve and are well described by an exponentially modified Gaussian distribution. The rescaled residual time-series for all the cities further exhibit certain robust dynamical features, with similar decay of auto-correlation functions, and power spectral densities displaying a similar 1/f decay at the tails. Finally, we propose a minimal stochastic model for the residual dynamics, which explains the observed universal features -- the stationary distribution, temporal correlation, and spectral scaling.

physics.soc-ph↗

arXiv2025

Classifying Urban Regions by Aggregated Pollutant Weather Correlation Strength: A Spatiotemporal Study

Understanding pollutant meteorology interactions is essential for environmental risk assessment. This study develops an entropy-based statistical framework to analyze static and temporal dependencies between urban air pollutants and meteorological variables across multiple Indian cities. Dependence is quantified using complementary linear and nonlinear measures, including Pearson correlation, mutual information, and relative conditional entropy. A key methodological contribution is a PCA based composite indexing framework that integrates these heterogeneous metrics into a unified and interpretable correlation score. For each pollutant meteorological pair within a city, PCA is used to extract a joint variability index, while spatial variability is assessed by aggregating correlations across cities. These indices are further combined to derive a comprehensive city-level correlation score that represents overall pollutant meteorology coupling strength and enables classification of cities into distinct interaction regimes. Sensitivity analysis, performed by systematically excluding individual variable pairs, demonstrates the robustness of the framework, with no single pair exerting disproportionate influence. Temporal dependencies are examined using transfer entropy and time-delayed mutual information. Results indicate that relative humidity generally leads changes in pollutant concentrations, whereas ambient temperature tends to lag, highlighting contrasting causal influences. Mutual information peaks at zero lag and decays rapidly, indicating strong short term interactions with limited persistence. Overall, the proposed framework provides a unified and interpretable approach for assessing complex pollutant meteorology interactions across diverse locations and time.

physics.soc-ph↗

arXiv2025

Entropy-Based Analysis of Urban Pollutant-Weather Correlations

We employ statistical physics and information-theoretic methods to quantify the dependencies between key atmospheric pollutants and meteorological variables across multiple Indian cities. To capture both linear and nonlinear relationships, we introduce a Composite Correlation Index (CCI) that combines the Pearson correlation coefficient with entropy-based measures, including mutual information and conditional entropy. Based on the CCI values, cities are clustered into distinct groups, uncovering regional similarities in pollutant-meteorology interactions that may reflect shared climatic or environmental conditions. To explore temporal structure and causal dynamics, we analyze the relationship between particulate matter (PM2.5) and relative humidity (RH) using transfer entropy, which reveals a bidirectional flow of information in most locations. Further time-domain analysis via time-delayed mutual information shows that, in many cities, the dependence between PM2.5 and RH peaks at zero lag and decays exponentially thereafter, indicating predominantly contemporaneous interactions with limited memory. This integrative framework provides a robust approach to characterizing atmospheric interaction regimes, bridging statistical physics with environmental complexity and revealing new insights into the pollutant-meteorology dynamics.

physics.soc-ph↗

arXiv2025

Exploring Citation Diversity in Scholarly Literature: An Entropy-Based Approach

This study explores the citation diversity in scholarly literature, analyzing different patterns of citations observed within different countries and academic disciplines. We examine citation distributions across top institutions within certain countries and find that the higher end of the distribution follows a Power Law or Pareto Law pattern; the scaling exponent of the Pareto Law varies depending on the number of top institutions included in the analysis. By adopting a novel entropy-based diversity measure, our findings reveal that countries with both small and large economies tend to cluster similarly in terms of citation diversity. The composition of countries within each group changes as the number of top institutions considered in the analysis varies. Moreover, we analyze citation diversity among award-winning scientists across six scientific disciplines, finding significant variations. We also explore the evolution of citation diversity over the past century across multiple fields. A gender-based study in several disciplines confirms varying citation diversities among male and female scientists. Our innovative citation diversity measure stands out as a valuable tool for assessing the unevenness of citation distributions, providing deeper insights that go beyond what traditional citation counts alone can reveal. This comprehensive analysis enhances our understanding of global scientific contributions and fosters a more equitable view of academic achievements.

physics.soc-ph↗

arXiv2025

An entropy based comparative study of regional and seasonal distributions of particulate matter in Indian cities

Particulate matter (PM), especially $\text{PM}_{2.5}$, is a critical air pollutant posing significant risks to human health and the environment in India. This study, using six years (2018-2024) of daily $\text{PM}_{2.5}$ data, investigates the seasonal characteristics of the distributions of $\text{PM}_{2.5}$ concentrations across eleven Indian cities, selected from different regions of the country. We find that, while each city has its own unique seasonal patterns, all of them show a universal exponential decay in the tail of the $\text{PM}_{2.5}$ distribution for all the seasons. However, the decay rates of this tail vary across cities, highlighting regional and seasonal disparities in pollution levels. To quantitatively characterize the {\it randomness} of the seasonal $\text{PM}_{2.5}$ concentration distributions, we compute Shannon entropy, a key information theoretic measure. This allows for classifying cities into different groups, according to the level of randomness observed in their seasonal distributions. To further explore the inter-city relationships, we employ Jensen-Shannon divergence (JSD), a symmetric measure of relative entropy, to quantitatively assess the degree of similarity in the $\text{PM}_{2.5}$ distributions among different cities. Remarkably, we find that several cities show very similar distributions in the winter months, which helps us to categories them into several groups. The groups obtained from these entropy based measures, namely, individual Shannon entropy and the JSD estimate, are consistent with each other, providing a robust framework for efficient air quality management and policy-making in India.

physics.soc-ph↗

arXiv2023

Kinetic Models of Wealth Distribution Having Extreme Inequality: Numerical Study of Their Stability Against Random Exchanges

In view of some persistent recent reports on a singular kind of growth of the world wealth inequality, where a finite (often handful) number of people tend to possess more than the wealth of the planet's 50\% population, we explore here if the kinetic exchange models of the market can ever capture such features where a significant fraction of wealth can concentrate in the hands of a countable few when the market size $N$ tends to infinity. One already existing example of such a kinetic exchange model is the Chakraborti or Yard-Sale model, where (in absence of tax redistribution etc) the entire wealth condenses in the hand of one (for any value of $N$), and the market dynamics stops. With tax redistribution etc, its steady state dynamics have been shown to have remarkable applicability in many cases of our extremely unequal world. We show here that another kinetic exchange model (called here the Banerjee model) has intriguing intrinsic dynamics, by which only ten rich traders or agents possess about 99.98\% of the total wealth in the steady state (without any tax etc like external manipulation) for any large value of $N$. We will discuss in some detail the statistical features of this model using Monte Carlo simulations. We will also show, if the traders each have a non-vanishing probability $f$ of following random exchanges, then these condensations of wealth (100\% in the hand of one agent in the Chakraborti model, or about 99.98\% in the hands ten agents in the Banerjee model) disappear in the large $N$ limit. We will also see that due to the built-in possibility of random exchange dynamics in the earlier proposed Goswami-Sen model, where the exchange probability decreases with an inverse power of the wealth difference of the pair of traders, one did not see any wealth condensation phenomena.

physics.soc-ph↗

arXiv2023

Role of Neighbouring Wealth Preference in Kinetic Exchange model of market

The kinetic exchange model has gained popularity in the field of statistical mechanics for investigating wealth interaction. Traditionally, kinetic exchange models have been studied without considering preferential interactions. However, in this study, we introduce two types of preferential interactions to explore wealth dynamics and its associated distributions. In the first preference, one agent is randomly selected, while the other agent is chosen randomly with wealth just above or below the first agent. Through this preference, we observe the emergence of a quasi-oligarchic society, where the majority of the wealth cycles around the hand of very few agents. For the second preference, we impose a constraint on the difference in pre-interaction wealth between the two agents. This preference leads to the segregation of society into two distinct economic classes. To investigate these phenomena, we conducted extensive Monte Carlo simulations, enabling us to characterize the behavior of wealth distributions in these two scenarios. Our findings shed light on the dynamics of wealth accumulation and distribution within preferential interactions in the context of the kinetic exchange model.

physics.soc-ph↗

arXiv2023

Sandpile Universality in Social Inequality: Gini and Kolkata Measures

Social inequalities are ubiquitous and evolve towards a universal limit. Herein, we extensively review the values of inequality measures, namely the Gini ($g$) index and the Kolkata ($k$) index, two standard measures of inequality used in the analysis of various social sectors through data analysis. The Kolkata index, denoted as $k$, indicates the proportion of the `wealth' owned by $(1-k)$ fraction of the `people'. Our findings suggest that both the Gini index and the Kolkata index tend to converge to similar values (around $g=k \approx 0.87$, starting from the point of perfect equality, where $g=0$ and $k=0.5$) as competition increases in different social institutions, such as markets, movies, elections, universities, prize winning, battle fields, sports (Olympics), etc., under conditions of unrestricted competition (no social welfare or support mechanism). In this review, we present the concept of a generalized form of Pareto's 80/20 law ($k=0.80$), where the coincidence of inequality indices is observed. The observation of this coincidence is consistent with the precursor values of the $g$ and $k$ indices for the self-organized critical (SOC) state in self-tuned physical systems such as sand piles. These results provide quantitative support for the view that interacting socioeconomic systems can be understood within the framework of SOC, which has been hypothesized for many years. These findings suggest that the SOC model can be extended to capture the dynamics of complex socioeconomic systems and help us better understand their behavior.

physics.soc-ph↗

arXiv2023

International Centre for the Advancement of Multidisciplinary Studies on Socio-Economic Systems

We start by summarising very briefly the various prior attempts (during the last one and half a decade), some of which were made as independent research centres and others as visiting centres with extensive visiting programs for luminaries from various basic sciences (Mathematics, Physics, Biology, Economics, and Sociology) and students from various institutions around the world for such interdisciplinary fusion of ideas and researches. Additionally, we briefly discuss the efforts that our institute has made (without any visible success so far, as in the other attempts elsewhere). We then emphasise the critical need for such an international centre to attract stalwarts in the basic disciplinary fields as well as interested students from around the world in order to comprehend the world's global socio-economic dynamics.

cond-mat.stat-mech↗

arXiv2022

Scaling Behavior of the Hirsch Index for Failure Avalanches, Percolation Clusters and Paper Citations

A popular measure for citation inequalities of individual scientists has been the Hirsch index ($h$). If for any scientist the number $n_c$ of citations is plotted against the serial number $n_p$ of the paper having those many citations (when the papers are ordered from highest cited to lowest) then $h$ corresponds to the nearest lower integer value of $n_p$ below the fixed point of the non-linear citation function (or given by $n_c = h = n_p$ if both $n_p$ and $n_c$ are dense set of integers near the $h$ value). The same index can be estimated (from $h=s=n_{s}$) for the avalanche or cluster of size ($s$) distributions ($n_s$) in elastic fiber bundle or percolation models. Another such inequality index, called the Kolkata index ($k$) says that $(1-k)$ fraction of papers attract $k$ fraction of citations ($k=0.80$ corresponds to the 80-20 law of Pareto). We find, for stress ($σ$), lattice occupation probability ($p$) or Kolkata index ($k$) near the bundle failure threshold ($σ_c$) or percolation threshold ($p_c$) or critical value of Kolkata index $k_c$, good fit to Widom-Stauffer like scaling $h/[\sqrt{N}/log N]$ = $f(\sqrt{N}[σ_c -σ]^α)$, $h/[\sqrt{N}/log N]=f(\sqrt{N}|p_c -p|^α)$ or $h/[\sqrt{N_c}/log N_c]=f(\sqrt{N_c}|k_c -k|^α)$ respectively, with asymptotically defined scaling function $f$, for systems of size $N$ (total number of fibers or lattice sites) or $N_c$ (total number of citations), and $α$ denoting the appropriate scaling exponent. We also show that if the number ($N_m$) of members of parliaments or national assemblies of different countries (with population $N$) is identified as their respective $h-$index, then the data fit the scaling relation $N_m \sim \sqrt N /log N$, resolving a major recent controversy.

physics.soc-ph↗

arXiv2022

Evolutionary Dynamics of Social Inequality and Coincidence of Gini and Kolkata indices under Unrestricted Competition

Social inequalities are ubiquitous and here we show that the values of the Gini ($g$) and Kolkata ($k$) indices, two generic inequality indices, approach each other (starting from $g = 0$ and $k = 0.5$ for equality) as the competitions grow in various social institutions like markets, universities, elections, etc. It is further showed that these two indices become equal and stabilize at a value (at $g = k \simeq 0.87$) under unrestricted competitions. We propose to view this coincidence of inequality indices as a generalized version of the (more than a) century old 80-20 law of Pareto. Furthermore, the coincidence of the inequality indices noted here is very similar to the ones seen before for self-organized critical (SOC) systems. The observations here, therefore, stand as a quantitative support towards viewing interacting socio-economic systems in the framework of SOC, an idea conjectured for years.

physics.soc-ph↗

arXiv2020

Inequality Measures: The Kolkata index in comparison with other measures

We provide a survey of the Kolkata index of social inequality, focusing in particular on income inequality. Based on the observation that inequality functions (such as the Lorenz function), giving the measures of income or wealth against that of the population, to be generally nonlinear, we show that the fixed point (like Kolkata index k) of such a nonlinear function (or related, like the complementary Lorenz function) offer better measure of inequality than the average quantities (like Gini index). Indeed the Kolkata index can be viewed as a generalized Hirsch index for a normalized inequality function and gives the fraction k of the total wealth possessed by the rich (1-k) fraction of the population. We analyze the structures of the inequality indices for both continuous and discrete income distributions. We also compare the Kolkata index to some other measures like the Gini coefficient and the Pietra index. Lastly, we provide some empirical studies which illustrate the differences between the Kolkata index and the Gini coefficient.

econ.GN↗

arXiv2019

On the Kolkata index as a measure of income inequality

We study the mathematical and economic structure of the Kolkata (k) index of income inequality. We show that the k-index always exists and is a unique fixed point of the complementary Lorenz function, where the Lorenz function itself gives the fraction of cumulative income possessed by the cumulative fraction of population (when arranged from poorer to richer). We show that the k-index generalizes Pareto's 80/20 rule. Although the k and Pietra indices both split the society into two groups, we show that k-index is a more intensive measure for the poor-rich split. We compare the normalized k-index with the Gini coefficient and the Pietra index and discuss when they coincide. We establish that for any income distribution the value of Gini coefficient is no less than that of the Pietra index and the value of the Pietra index is no less than that of the normalized k-index. While the Gini coefficient and the Pietra index are affected by transfers exclusively among the rich or among the poor, the k-index is only affected by transfers across the two groups.

econ.TH↗