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The distribution of wealth and income is never uniform, and philosophers and economists have tried for years to understand the reasons and formulate remedies for such inequalities. This book introduces the elegant and intriguing kinetic exchange models that physicists have developed to tackle these issues. This is the first monograph in econophysics focussed on the analyses and modelling of these distributions, and is ideal for physicists and economists. It is written in simple, lucid language, with plenty of illustrations and in-depth analyses, making it suitable for researchers new to this field as well as specialized readers. It explores the origin of economic inequality and examines the scientific steps that can be taken to reduce this inequality in the future.

In the present paper, we have investigated the effect of plasmonic gold nanoparticles (Au NPs) decoration on the photocatalytic efficiency of molybdenum disulfide (MoS 2 ) nanosheets. The Au NPs are grown on the surfaces of chemically exfoliated MoS 2 nanosheets by chemical reduction method with four different concentrations. The resulting Au-MoS 2 nanostructures (NSs) are then characterized by X-ray diffractometer, Raman spectrometer, absorption spectrophotometer, field emission scanning electron microscopy, energy dispersive X-ray, and transmission electron microscopy (TEM). Sizes of the exfoliated MoS 2 nanosheets are ~ 700 nm. In addition, the sizes of Au nanoparticles increase from 8.02 ± 2.03 nm to 9.81 ± 3.18 nm with the increase in concentrations of Au ions, as revealed by TEM imaging. Exfoliated MoS 2 and Au-MoS 2 NSs are used to study the photocatalytic degradation of organic dyes, methyl red (MR) and methylene blue (MB). Under UV–Visible light irradiation, pristine MoS 2 shows photodegradation efficiencies in the range of 30.0% to 46.9% for MR, and 23.3% to 44.0% for MB, with varying exposure times of 30 to 120 min. However, Au-MoS 2 NSs with the sets having maximum Au NPs concentrations, show enhanced degradation efficiencies from 70.2 to 96.7% for MR, and from 65.2 to 94.3% for MB. The degradation rate constants vary from − 0.5660 to − 1.5551 min −1 for MR dye, and vary from − 0.3587 to − 1.2614 min −1 for MB dye. The multi-fold enhancements of degradation efficiencies for both the dyes with Au-MoS 2 NSs, can be attributed to the presence of Au NPs acting as charge trapping sites in the NSs. We believe this type of study could provide a way to battle the ill-effects of environmental degradation that pose a major threat to humans as well as biodiversity. This study can be further extended to other semiconducting materials in conjugation with two dimensional materials for photocatalytic treatment of polluted water.

The study of the critical dynamics in complex systems is always interesting yet challenging. Here, we choose financial markets as an example of a complex system, and do comparative analyses of two stock markets-the S&P 500 (USA) and Nikkei 225 (JPN). Our analyses are based on the evolution of cross-correlation structure patterns of short-time epochs for a 32 year period (1985-2016). We identify 'market states' as clusters of similar correlation structures, which occur more frequently than by pure chance (randomness). The dynamical transitions between the correlation structures reflect the evolution of the market states. Power mapping method from the random matrix theory is used to suppress the noise on correlation patterns, and an adaptation of the intra-cluster distance method is used to obtain the 'optimum' number of market states. We find that the S&P 500 is characterized by four market states and Nikkei 225 by five. We further analyze the co-occurrence of paired market states; the probability of remaining in the same state is much higher than the transition to a different state. The transitions to other states mainly occur among the immediately adjacent states, with a few rare intermittent transitions to the remote states. The state adjacent to the critical state (market crash) may serve as an indicator or a 'precursor' for the critical state and this novel method of identifying the long-term precursors may be helpful for constructing the early warning system in financial markets, as well as in other complex systems.

Random matrix theory has been widely applied in physics, and even beyond physics. Here, we apply such tools to study catastrophic events, which occur rarely but cause devastating effects. It is important to understand the complexity of the underlying dynamics and signatures of catastrophic events in complex systems, such as the financial market or the environment. We choose the USA S&P-500 and Japanese Nikkei-225 financial markets, as well as the environmental ozone system in the USA. We study the evolution of the cross-correlation matrices and their eigen spectra over different short time-intervals or 'epochs'. A slight non-linear distortion is applied to the correlation matrix computed for any epoch, leading to the emerging spectrum of eigenvalues, mainly around zero. The statistical properties of the emerging spectrum are intriguing-the smallest eigenvalues and the shape of the emerging spectrum (characterized by the spectral entropy) capture the system instability or criticality. Importantly, the smallest eigenvalue could also signal a precursor to a market catastrophe as well as a 'market bubble'. We demonstrate in two paradigms the capacity of the emerging spectrum to understand the nature of instability; this is a new and robust feature that can be broadly applied to other physical or complex systems.

News reports in media contain records of a wide range of socio-economic and political events in time. Using a publicly available, large digital database of news records, and aggregating them over time, we study the network of ethnic conflicts and human rights violations. Complex network analyses of the events and the involved actors provide important insights on the engaging actors, groups, establishments and sometimes nations, pointing at their long range effect over space and time. We find power law decays in distributions of actor mentions, co-actor mentions and degrees and dominance of influential actors and groups. Most influential actors or groups form a giant connected component which grows in time, and is expected to encompass all actors globally in the long run. We demonstrate how targeted removal of actors may help stop spreading unruly events. We study the cause-effect relation between types of events, and our quantitative analysis confirm that ethnic conflicts lead to human rights violations, while it does not support the converse.

We demonstrate the existence of an empirical linkage between nominal financial networks and the underlying economic fundamentals, across countries. We construct the nominal return correlation networks from daily data to encapsulate sector-level dynamics and infer the relative importance of the sectors in the nominal network through measures of centrality and clustering algorithms. Eigenvector centrality robustly identifies the backbone of the minimum spanning tree defined on the return networks as well as the primary cluster in the multidimensional scaling map. We show that the sectors that are relatively large in size, defined with three metrics, viz., market capitalization, revenue and number of employees, constitute the core of the return networks, whereas the periphery is mostly populated by relatively smaller sectors. Therefore, sector-level nominal return dynamics are anchored to the real size effect, which ultimately shapes the optimal portfolios for risk management. Our results are reasonably robust across 27 countries of varying degrees of prosperity and across periods of market turbulence (2008–09) as well as periods of relative calmness (2012–13 and 2015–16).

The topological characteristics of biological networks enable us to identify the key nodes in terms of modularity. However, due to a large size of the biological networks with many hubs and functional modules across intertwined layers within the network, it often becomes difficult to accomplish the task of identifying potential key regulators. We use for the first time a generalized formalism of Hamiltonian Energy (HE) with a recursive approach. The concept, when applied to the Apoptosis Regulatory Gene Network (ARGN), helped us identify 11 Motif hubs (MHs), which influenced the network up to motif levels. The approach adopted allowed to classify MHs into 5 significant motif hubs (S-MHs) and 6 non-significant motif hubs (NS-MHs). The significant motif hubs had a higher HE value and were considered as high-active key regulators; while the non-significant motif hubs had a relatively lower HE value and were considered as low-active key regulators, in network control mechanism. Further, we compared the results of the HE analyses with the topological characterization, after subjecting to the three conditions independently: (i) removing all MHs, (ii) removing only S-MHs, and (iii) removing only NS-MHs from the ARGN. This procedure allowed us to cross-validate the role of 5 S-MHs, NFk-B1, BRCA1, CEBPB, AR, and POU2F1 as the potential key regulators. The changes in HE calculations further showed that the removal of 5 S-MHs could cause perturbation at all levels of the network, a feature not discernible by topological analysis alone.

Financial markets, being spectacular examples of complex systems, display rich correlation structures among price returns of different assets. The correlation structures change drastically, akin to critical phenomena in physics, as do the influential stocks (leaders) and sectors (communities), during market events like crashes. It is crucial to detect their signatures for timely intervention or prevention. Here we use eigenvalue decomposition and eigen-entropy, computed from eigenvector centralities of different stocks in the cross-correlation matrix, to extract information about the disorder in the market. We construct a ‘phase space’, where different market events (bubbles, crashes, etc) undergo phase separation and display order–disorder movements. An entropy functional exhibits scaling behavior. We propose a generic indicator that facilitates the continuous monitoring of the internal structure of the market—important for managing risk and stress-testing the financial system. Our methodology would help in understanding and foreseeing tipping points or fluctuation patterns in complex systems.

In the light of contemporary discussions of inter and trans disciplinarity, this paper approaches econophysics and sociophysics to seek a response to the question – whether these interdisciplinary fields could contribute to physics and economics. Drawing upon the literature on history and philosophy of science, the paper argues that the two way traffic between physics and economics has a long history and this is likely to continue in the future.

Many existing studies on pattern formation in the reaction-diffusion systems rely on deterministic models. However, environmental noise is often a major factor which leads to significant changes in the spatiotemporal dynamics. In this paper, we focus on the spatiotemporal patterns produced by the predator-prey model with ratio-dependent functional response and density dependent death rate of predator. We get the reaction-diffusion equations incorporating the self-diffusion terms, corresponding to random movement of the individuals within two dimensional habitats, into the growth equations for the prey and predator population. In order to have the noise added model, small amplitude heterogeneous perturbations to the linear intrinsic growth rates are introduced using uncorrelated Gaussian white noise terms. For the noise added system, we then observe spatial patterns for the parameter values lying outside the Turing instability region. With thorough numerical simulations we characterize the patterns corresponding to Turing and Turing-Hopf domain and study their dependence on different system parameters like noise-intensity, etc.