Searcharxiv⌕ Search

arXiv subjects

Bikas K. Chakrabarti

Publications and source records attributed to Bikas K. Chakrabarti.

At least 19 recordsLinked to original sources

Social Physics: A manifesto

Social Physics seeks quantitative, empirically testable explanations of collective human behavior. Its name has a long and contested history, but its contemporary program is neither the claim that society is literally a physical system nor an attempt to replace the social sciences with physics. It is an interdisciplinary practice: observation and experimentation, model construction, mathematical and computational analysis, and repeated confrontation with data. The field has been transformed by analyzing digital traces, network science, agent-based modeling, large-scale experiments, and the capacity to study coupled dynamics across economic, social, technological, biological, and physical layers. We review advances in financial analysis and modeling; economic complexity; the structure and evolution of social networks; spreading, opinion, and information dynamics; inequality, cooperation, conflict, mobility, cities, culture, science, and collective behavior; and the emerging study of human-AI ecosystems. Across these domains, common features recur - heterogeneity, interaction, feedback, adaptation, non-equilibrium dynamics, multiscale organization, and emergent collective outcomes. We also confront the limitations that have arisen in this field: convenience samples, platform dependence, weak causal identification, over-universal claims, insufficient engagement with meaning and institutions, privacy risks, and the danger that predictive models become instruments of manipulation. We propose a future Social Physics organized around theory - data reciprocity; causal and generative explanation; measurement validity and cross-context generalization; responsible, participatory data governance; genuinely interdisciplinary collaboration; and reflexive study of interventions and algorithms that alter the systems being observed.

physics.soc-ph↗

Normalized fractional Hirsch Index and Modified Pareto Law

The Hirsch index (introduced in 2005) has been a very successful scientometric author-level measure for the publication impact inequalities among the authors. However, it does not have any upper bound and statistically it grows in proportion to the square root of the number of publications by the author. Social scientists, on the other hand, measure the economic performance of different countries (having different wealth amounts and populations etc.) using inequality indices like the Gini index (since 1912) etc., which are normalized quantities (independent of the country's total wealth or the population size). We show here that a normalized fractional Hirsch index, giving the fraction of total citations earned by fraction of those successful papers published by the author, can even indicate that typically about $14\%$ of the top cited papers earn about $86\%$ of citations for very successful scientists (like the 95 Nobel Laureates considered here). This is similar to Pareto's 80-20 law (since 1896) and agrees more precisely with those observed for self-organized sandpile models, where typically $86\%$ of the avalanche masses are dissipated through $14\%$ of the largest avalanches as the piles approach their respective self-organized critical points.

physics.soc-ph↗

Estimates of ground state energies for the quantum SK and 2D-EA models, using deGennes-Suzuki-Kubo mean-field annealing dynamics

We perform large scale quantum annealing of the Sherrington-Kirkpatrick (SK) spin glass up to a system size $N=40000$ to estimate its ground state energy using the deGennes-Suzuki-Kubo mean-field quantum Ising dynamics, extending the earlier results (reported in Eur. Phys. J. B {\bf 98}, 226 (2025)). Here we numerically solve the deGennes-Suzuki-Kubo annealing dynamics to obtain the spin configurations and subsequently the ground state energy for a given system size at the end of the annealing, starting from a quantum paramagnetic state. The method shows high efficiency, with an overall algorithmic cost of $O(N^3)$ in estimating the energy of the ground state. We later extend this quantum annealing study to estimate the ground state energies (starting again from the quantum paramagnetic phase, annealing down to any desired low value of the transverse field) for the Edwards-Anderson (EA) spin glass model on a square lattice.

cond-mat.dis-nn↗

Models and Measures of Statistical Physics and Sociophysics for Fracture Mechanics and Earthquake Dynamics: An Introduction

The breaking or fracture of materials and damages or devastations due to earthquakes have caught our attention since the earliest stage of human civilization. In fact, at around 1500, Leonardo Da Vinci made the pioneering observation that, unlike elastic constants (formalized later by Hooke in 1678) of the materials, the tensile (breaking) strengths of nominally identical iron wires decrease drastically with their length, indicating the vanishing breaking strength of materials in the large size limit, suggesting the impossibility of constructing arbitrarily large structures. This was the first observation that unlike the elasticity of disordered materials, which remains defined in the thermodynamic limit (self averaging statistics), the breaking properties of the disordered materials have extreme (non self averaging) statistics. In spite of major and some precise developments in statistical physical modelling and characterizing the fracture mechanics (starting with Allan Griffith's crack nucleation theory in 1921 and the weakest link failure Fibre Bundle Model of Frederick Thomas Peirce in 1926) and of earthquake dynamics (starting with Robert Burridge and Leon Knopoff's continuum dynamical model in 1967 and later other discrete or lattice train models or fractal overlap models of stick slip earthquakes), no graduate level textbook in condensed matter physics or in statistical physics introduces the basic models and their properties. And now computer scientists and social scientists (coming with their social inequality measures applied to the avalanche statistics in precursor failures) are joining their efforts to explore the new precursory inequality measures for big avalanches or failures. This introductory review is designed to fill this gap with a view to introducing these to this wider audience and to take them to the current frontiers in these fields.

cond-mat.stat-mech↗

Relations Between the Inequality Indices Gini, Pietra and Kolkata: Theory and Data Analysis

We study relations between three inequality indices, namely the Gini ($g$), Pietra ($p$) and Kolkata ($k$) introduced in 1912, 1915 and 2014 respectively and all are derived from the Lorenz function $L(x)$ introduced in 1905. The Kolkata index (which corresponds to a fixed point of the complementary Lorenz function $L_c(x) \equiv 1-L(x)$) gives the fraction $k$ of wealth possessed by the richest $1-k$ fraction of people ($k$ = 0.8 corresponds to Pareto's 80-20 law from 1896). We show rigorously that while the Pietra index value $p$ should be greater than or equal to $2k-1$, the Robin Hood index should strictly be equal to the excess wealth fraction $2k-1$ possessed by the richest $1-k$ fraction of people. Our numerical data analysis for US IRS Income data (1983-2022), Bollywood (India) movie income data (1999-2024) and the citation inequalities across the publications by forty Nobel Laureates (2020-2025) in Economics, Physics, Chemistry and Medicine clearly show that $p/(2k-1)$ is always greater than unity but the deviation is never more than five percent. Assuming some simple analytic form for the Lorenz function, we also derived the relations $k = (1/2) + (3/8)g$ for small $g$ values and $p/g = 3/4$. However, by considering the Lorenz function appropriate for the generalized Pareto power law distribution, we obtain an extended range ($1_+ < p/g \leq e/2$) that captures most of the empirical data.

physics.soc-ph↗

deGennes-Suzuki-Kubo Quantum Ising Mean Field Dynamics: Applications to Quantum Hysteresis, Heat Engines and Annealing

We briefly review the early development of the mean-field dynamics for cooperatively interacting quantum many-body systems, mapped to pseudo-spin (Ising-like) systems. We start with (Anderson, 1958) pseudo-spin mapping of the BCS (1957) Hamiltonian of superconductivity, reducing it to a mean-field Hamiltonian of XY (or effectively Ising) model in a transverse field. Then we get the mean-field estimate for the equilibrium gap in the ground state energy at different temperatures (gap disappearing at the transition temperature), which fits Landau's (1949) phenomenological theory of superfluidity. We then present in detail a general dynamical extension (for non-equilibrium cases) of the mean-field theory of quantum Ising systems (in a transverse field), following de Gennes' (1963) decomposition of the mean field into orthogonal classical cooperative (longitudinal) component and the quantum (transverse) component, with each component following Suzuki--Kubo (1968) mean-field dynamics. Next we discuss its applications to quantum hysteresis in Ising magnets (in presence of an oscillating transverse field), to quantum heat engines (employing transverse Ising model as working fluid), and to the quantum annealing of the Sherrington--Kirkpatrick (1975) spin glass by tuning down (to zero) the transverse field, which provides a very fast computational algorithm leading to ground state energy values converging to the best known analytic estimate for the model. Finally, we summarize the main results obtained and conclude about the effectiveness of the de Gennes--Suzuki--Kubo mean-field equations for the study of various dynamical aspects of quantum condensed matter systems.

cond-mat.stat-mech↗

Quantum Annealing in SK Model Employing Suzuki-Kubo-deGennes Quantum Ising Mean Field Dynamics

We study a quantum annealing approach for estimating the ground state energy of the Sherrington-Kirpatrick mean field spin glass model using the Suzuki-Kubo-deGennes dynamics applied for individual local magnetization components. The solutions of the coupled differential equations, in discretized state, give a fast annealing algorithm (cost $N^3$) in estimating the ground state of the model: Classical ($E^0= -0.7629 \pm 0.0002$), Quantum ($E^0=-0.7623 \pm 0.0001$) and Mixed ($E^0=-0.7626 \pm 0.0001$), all of which are to be compared with the best known estimate $E^0= -0.763166726 \dots$ . We infer that the continuous nature of the magnetization variable used in the dynamics here is the reason for reaching close to the ground state quickly and also the reason for not observing the de-Almeida-Thouless line in this approach.

cond-mat.dis-nn↗

Classical Annealing of Sherrington-Kirkpatrick Spin Glass Using Suzuki-Kubo Mean-field Ising Dynamics

We propose and demonstrate numerically a fast classical annealing scheme for the Sherrington-Kirkpatrick (SK) spin glass model, employing the Suzuki-Kubo meanfield Ising dynamics (supplemented by a modified Thouless-Anderson-Palmer reaction field). The resultant dynamics, starting from any arbitrary paramagnetic phase (with local magnetizations $m_i=\pm 1$ for the $i^{th}$ spin, and the global magnetization $m=0$), takes the system quickly to an appropriate state with small local values of magnetization ($m_i$) commensurate with the (frustrated) interactions. As the temperature decreases with the annealing, the configuration practically remains (in an effective adiabatic way) close to a low energy configuration as the magnitudes of $m_i$'s and the spin glass order parameter $q$ grow to unity. While the configuration reached by the procedure is not the ground state, for an $N$-spin SK model (with $N$ up to 10000) the deviation in the energy per spin $E^0_N - E^0$ found by the annealing procedure scales as $N^{-2/3}$, with $E^0 = -0.7629\pm 0.0002$, suggesting that in the thermodynamic limit the energy per spin of the low energy configurations converges to the ground state of the SK model (analytical estimate being $E^0 =-0.7631667265 \dots$), fluctuation $σ_N $ in $E^0_N$ decreases as $\sim N^{-3/4}$ and the annealing time $τ_N \sim N$, making this protocol highly efficient in estimating the ground state of the SK model.

cond-mat.dis-nn↗

Does Excellence Correspond to Universal Inequality Level?

We study the inequality of citations received for different publications of various researchers and Nobel laureates in Physics, Chemistry, Medicine and Economics using Google Scholar data from 2012 to 2024. Citation distributions are found to be highly unequal, with even greater disparity among Nobel laureates. Measures of inequality, such as the Gini and Kolkata indices, emerge as useful indicators for distinguishing Nobel laureates from others. Such high inequality corresponds to growing critical fluctuations, suggesting that excellence aligns with an imminent (self-organized dynamical) critical point. Additionally, Nobel laureates exhibit systematically lower values of the Tsallis--Pareto parameter \( b \) and Shannon entropy, indicating more structured citation distributions. We also analyze the inequality in Olympic medal tallies across countries and find similar levels of disparity. Our results suggest that inequality measures can serve as proxies for competitiveness and excellence.

physics.soc-ph↗

Signature of maturity in cryptocurrency volatility

We study the fluctuations, particularly the inequality of fluctuations, in cryptocurrency prices over the last ten years. We calculate the inequality in the price fluctuations through different measures, such as the Gini and Kolkata indices, and also the $Q$ factor (given by the ratio between the highest value and the average value) of these fluctuations. We compare the results with the equivalent quantities in some of the more prominent national currencies and see that while the fluctuations (or inequalities in such fluctuations) for cryptocurrencies were initially significantly higher than national currencies, over time the fluctuation levels of cryptocurrencies tend towards the levels characteristic of national currencies. We also compare similar quantities for a few prominent stock prices.

physics.soc-ph↗

Q-factor: A measure of competition between the topper and the average in percolation and in SOC

We define the $Q$-factor in the percolation problem as the quotient of the size of the largest cluster and the average size of all clusters. As the occupation probability $p$ is increased, the $Q$-factor for the system size $L$ grows systematically to its maximum value $Q_{max}(L)$ at a specific value $p_{max}(L)$ and then gradually decays. Our numerical study of site percolation problems on the square, triangular and the simple cubic lattices exhibits that the asymptotic values of $p_{max}$ though close, are distinctly different from the corresponding percolation thresholds of these lattices. We have also shown using the scaling analysis that at $p_{max}$ the value of $Q_{max}(L)$ diverges as $L^d$ ($d$ denoting the dimension of the lattice) as the system size approaches to their asymptotic limit. We have further extended this idea to the non-equilibrium systems such as the sandpile model of self-organized criticality. Here, the $Q(ρ,L)$-factor is the quotient of the size of the largest avalanche and the cumulative average of the sizes of all the avalanches; $ρ$ being the drop density of the driving mechanism. This study has been prompted by some observations in Sociophysics.

cond-mat.stat-mech↗

Quantum Ising Heat Engines: A mean field study

We have studied the efficiencies of both classical and quantum heat engines using an Ising model as working fluid and the mean field equation for its non-equilibrium dynamics, formulated earlier\cite{acs,ac} to study the dynamical hysteresis and the dynamical phase transitions in the quantum Ising ferromagnets. We studied numerically the Ising magnet's nonintegrable coupled nonlinear first order differential equations of motion for a four stroke heat engine and compared the efficiencies in both classical and quantum limits using the quasi-static approximation. In both the pure classical and pure quantum cases, the numerically calculated efficiencies are much less than the corresponding Carnot values. Our analytical formulations of the efficiencies (both in pure classical as well as in pure quantum Ising heat engines) are found to agree well with the numerical estimates. Such formulations also indicate increased efficiency for the mixed case of a transverse field driven Ising engine in presence of nonzero longitudinal field. We also numerically checked and found that the efficiency of such a (mixed) quantum Ising heat engine can indeed have much higher efficiency for appropriate values of the transverse and longitudinal fields.

cond-mat.stat-mech↗

Achieving Maximum Utilization in Optimal Time for Learning or Convergence in the Kolkata Paise Restaurant Problem

The objective of the KPR agents are to learn themselves in the minimum (learning) time to have maximum success or utilization probability ($f$). A dictator can easily solve the problem with $f = 1$ in no time, by asking every one to form a queue and go to the respective restaurant, resulting in no fluctuation and full utilization from the first day (convergence time $τ= 0$). It has already been shown that if each agent chooses randomly the restaurants, $f = 1 - e^{-1} \simeq 0.63$ (where $e \simeq 2.718$ denotes the Euler number) in zero time ($τ= 0$). With the only available information about yesterday's crowd size in the restaurant visited by the agent (as assumed for the rest of the strategies studied here), the crowd avoiding (CA) strategies can give higher values of $f$ but also of $τ$. Several numerical studies of modified learning strategies actually indicated increased value of $f = 1 - α$ for $α\to 0$, with $τ\sim 1/α$. We show here using Monte Carlo technique, a modified Greedy Crowd Avoiding (GCA) Strategy can assure full utilization ($f = 1$) in convergence time $τ\simeq eN$, with of course non-zero probability for an even larger convergence time. All these observations suggest that the strategies with single step memory of the individuals can never collectively achieve full utilization ($f = 1$) in finite convergence time and perhaps the maximum possible utilization that can be achieved is about eighty percent ($f \simeq 0.80$) in an optimal time $τ$ of order ten, even when $N$ the number of customers or of the restaurants goes to infinity.

cs.GT↗

Finding critical points and correlation length exponents using finite size scaling of Gini index

The order parameter for a continuous transition shows diverging fluctuation near the critical point. Here we show, through numerical simulations and scaling arguments, that the inequality (or variability) between the values of an order parameter, measured near a critical point, is independent of the system size. Quantification of such variability through Gini index ($g$), therefore, leads to a scaling form $g=G\left[|F-F_c|N^{1/dν}\right]$, where $F$ denotes the driving parameter for the transition (e.g., temperature $T$ for ferromagnetic to paramagnetic transition transition, or lattice occupation probability $p$), $N$ is the system size, $d$ is the spatial dimension and $ν$ is the correlation length exponent. We demonstrate the scaling for the Ising model in two and three dimensions, site percolation on square lattice and the fiber bundle model of fracture.

cond-mat.stat-mech↗

A Fiber Bundle Model of Systemic Risk in Financial Networks

Failure statistics of banks in the US show that their sizes are highly unequal (ranging from a few tens of thousands to over a billion dollars) and also, they come in `waves' of intermittent activities. This motivates a self-organized critical picture for the interconnected banking network. For such dynamics, recent developments in studying the inequality of the events, measured through the well-known Gini index and the more recently introduced Kolkata index, have been proved to be fruitful in anticipating large catastrophic events. In this chapter we review such developments for catastrophic failures using a simple model called the fiber bundle model. We then analyze the failure data of banks in terms of the inequality indices and study a simple variant of the fiber bundle model to analyze the same. It appears, both from the data and the model, that coincidence of these two indices signal a systemic risk in the network.

physics.soc-ph↗

Do Successful Researchers Reach the Self-Organized Critical Point?

The index of success of the researchers is now mostly measured using the Hirsch index ($h$). Our recent precise demonstration, that statistically $h \sim \sqrt {N_c} \sim \sqrt {N_p}$, where $N_p$ and $N_c$ denote respectively the total number of publications and total citations for the researcher, suggests that average number of citations per paper ($N_c/N_p$), and hence $h$, are statistical numbers (Dunbar numbers) depending on the community or network to which the researcher belongs. We show here, extending our earlier observations, that the indications of success are not reflected by the total citations $N_c$, rather by the inequalities among citations from publications to publications. Specifically, we show that for very successful authors, the yearly variations in the Gini index ($g$, giving the average inequality of citations for the publications) and the Kolkata index ($k$, giving the fraction of total citations received by the top $1 - k$ fraction of publications; $k = 0.80$ corresponds to Pareto's 80/20 law) approach each other to $g = k \simeq 0.82$, signaling a precursor for the arrival of (or departure from) the Self-Organized Critical (SOC) state of his/her publication statistics. Analyzing the citation statistics (from Google Scholar) of thirty successful scientists throughout their recorded publication history, we find that the $g$ and $k$ for very successful among them (mostly Nobel Laureates, highest rank Stanford Cite-Scorers, and a few others) reach and hover just above (and then) below that $g = k \simeq 0.82$ mark, while for others they remain below that mark. We also find that all the lower (than the SOC mark 0.82) values of $k$ and $g$ fit a linear relationship $k = 1/2 + cg$, with $c = 0.39$.

cs.DL↗

Kinetic Exchange Models of Income and Wealth Distribution: Self Organization and Poverty Level

In this invited book chapter, we draw the reader to a brief review of the different Kinetic Exchange Models (KEMs) that have gradually developed for markets and how they can be employed to quantitatively study inequalities (the Gini Index and the Kolkata Index) that pervade real economies. Since a many-body economical market can be studied using tested laws of physics, these models have the freedom to incorporate provisions like inclusion of individual saving behaviors while trading and rendering these saving behaviors to be time-independent and time-dependent respectively. This is to observe when and how the well known exponential distribution for no-saving gives rise to a distribution with a most probable income. A review of the earlier cases along with their implementation with a bias, where the population in the low-income bracket of the society is favored by selecting one of the traders in the trading process to be the poorest of all, follows. The biased selection of agents ultimately giving rise to self-organizing features in the money distribution has also been reviewed in detail, using the behavior of the Self-Organized Poverty Level. In the end, we elucidate the recent endeavors of the KEMs in finding answers to the growing condensation of wealth in the hands of a countable few rich people and providing probable solutions that can curb further expansion of oligarchic societies.

physics.soc-ph↗

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↗