The Physics of Cities
Fabiano L. Ribeiro, Matjaž Perc, and Haroldo V. Ribeiro
Frontiers in Physics 10, 964701 (2022)
Complex SystemsEditorialScaling LawsUrban IndicatorsUrban Metrics
The word “physics” can be understood in at least two ways. First, based on the Greek origin of the word, physics means nature. Accordingly, when we state our intention to understand the physics of a phenomenon, we want to know how and why it behaves as it does. In other words, understanding the nature of something – be it a natural phenomenon or a concept – means that we comprehend the mechanisms governing the underlying system. The second meaning of the word “physics” is related to the field of study or knowledge area; that is, to all theoretical and experimental tools developed by physicists to understand our universe. These two meanings of the word “physics”, to some extent, appropriately describe a research area that has been highly active in recent years and is aimed at understanding the nature of cities through theoretical tools from physics. Many believe these studies mark the birth of a new discipline – a “new science of cities” – that aims to understand cities from the complexity science perspective.
Indeed, in the last few years, the physics community has made a breakthrough in understanding urban phenomena. In part, this ongoing progress is a consequence of a progressive and expressive increase in the amount of data available regarding the dynamics of urban life, but it is also driven by the necessity of unified theories to explain and propose experiments. These two elements, a massive volume of data and theories, which are so familiar to physicists, are essential for researchers to develop systematic ways to identify, describe, and explain commonalities, regularities, and universal patterns in cities – goals that were central to this Research Topic.
This special issue started with the article of Operti et al., which proposed a novel methodology to define and quantify the topography of racial residential segregation in large urban areas. By applying their method to New York City and using data from 1990 to 2010, Operti et al. investigated the dynamics of racial segregation for four racial categories as well as how it correlates with income, property values, and gentrification within neighborhoods. They reported that income inequality is higher in regions with high population densities of two or more races and that a positive flux of white citizens associates with an increase in property values, while the opposite is observed for places with a positive flux of black citizens. Furthermore, their approach also allowed the identification of the two largest displacements of black citizens and the emergence of gentrified regions.
The second contribution was made by Hayata, who focused on the empirical distributions of population, population density, and area of Japanese municipalities broken down into the 47 prefectures (regions or provinces) that constitute the country. Hayata used rank-size plots (also called Zipf plots) and tested different rank-size rules for the municipalities with a particular interest in urban areas. The author further considered that cities are competing for the extension of their areas and proposed a simple model inspired by sports tournaments, which in turn motivated an analysis of urban area evolution in the view of global warming and consequent shrinking of the land sizes.
Gere et al. contributed the third article of this collection where wealth distribution in villages of the commune Sâncraiu (Kalotaszentkirály) – a well-delimited region in Transylvania (Romania) – was studied using a unique dataset spanning radically different economic contexts: before collectivization imposed by communist (1961), the latest year of the communist regime in Romania (1989), and the current situation after over 30 years of the free-market economy (2021). Using an exactly solvable master equation, the authors were capable of realistically describing income dynamics and its distribution as well as discussing the observed socioeconomic changes. Among other findings, Gere et al. reported that the “rich gets richer” or the Matthew effect emerges with the fall of communism, which in turn is modeled as a linear growth rate.
In the fourth work of this research topic, Bassolas et al. also focused on spatial segregation, but instead of race, they investigated the spatial heterogeneity of different income categories in United States cities based on diffusion and synchronization dynamics occurring over a graph, where nodes are spatial units and connections indicate spatially adjacent units. Bassolas et al. used the time needed to reach the synchronization to quantify spatial heterogeneity, and among other findings, they reported that low- and high-income categories are more segregated in space than middle-income categories. Curiel, Cabrera-Arnau, and Bishop contributed the fifth article of this collection, in which the impact of city size on nearby cities was addressed using data from over two thousand African cities. The authors constructed the urban road network among these cities and proposed an approach to determine regions of influence of cities from this network. They then used urban scaling models to investigate the relationship between city size and characteristics of their regions of influence, finding that the size of a city impacts not only its urban indicators but also the indicators of neighboring cities. In particular, they reported that large cities drive urban emergence and growth of other cities even hundreds of kilometers apart.
Finally, the article by Molinero closed this special issue by presenting an analytical framework based on fractal theory to model urban growth. This theoretical approach was capable of describing many features of cities, including scaling laws with population size and the fractal nature of cities, and proved helpful in modeling urban growth with a case set on the United Kingdom system.
This Frontiers special issue has thus shed light on different urban phenomena through the unique lens of complexity science and physics. The published papers have contributed to the identification of novel regularities and connections between city properties, and we hope they will positively impact decision-making by public planners to optimize infrastructure and foster the economic development of urban areas.
We need more empirical investigations and model validation for a better understanding of crime - Comment on 'Statistical physics of crime: A review' by M.R. D'Orsogna and M. Perc.
Since the seminal works of Wilson and Kelling  in 1982, the “broken windows theory” seems to have been widely accepted among the criminologists and, in fact, empirical findings actually point out that criminals tend to return to previously visited locations. Crime has always been part of the urban society’s agenda and has also attracted the attention of scholars from social sciences ever since. Furthermore, over the past six decades the world has experienced a quick and notorious urbanization process: by the eighties the urban population was about 40% of total population, and today more than half (54%) of the world population is urban . The urbanization has brought us many benefits such as better working opportunities and health care, but has also created several problems such as pollution and a considerable rise in the criminal activities. In this context of urban problems, crime deserves a special attention because there is a huge necessity of empirical and mathematical (modeling) investigations which, apart from the natural academic interest, may find direct implications for the organization of our society by improving political decisions and resource allocation.
Despite being a naturally interdisciplinary topic, the idea of a physicist studying crime may still cause some surprise (despite the fact that physicists have investigated, more than ever, several systems very far from the traditional domain of physics), but the review by D’Orsogna and Perc  shows us that several collective patterns related to crimes are analogous to those exhibited by classical physical systems such as the reaction–diffusion equations, which model the evolution of chemicals under chemical reactions and diffusion, but also describe the evolution of crime hotspots. D’Orsogna and Perc bring us a concise and general view of the recent applications of mathematical methods for modeling crime related problems. The review covers the modeling of crime hotspots by generalized reaction–diffusion equations and by self-exciting point process; presents an overview of the evolutionary game theory for addressing crime as a social dilemma; illustrates the use of network tools for understanding criminal organizations; and, by combining these tools with random walks methods, demonstrates how it is possible to infer the network topology of street gangs. Finally, within a more sociological view, the authors discuss the role of punishment for rehabilitation and to prevent recidivism.
What I found special in this review is that the authors do not only stay in the “physicists’ comfort zone”, that is, too focused on models and proprieties that resemble those of phase transitions, which are beautiful for theoretical physicists but much less interesting for creating methods and tools to help us prevent and understand crimes from a more social perspective. D’Orsogna and Perc drive us towards an empirical and applied approach by reviewing and discussing several sociological concepts of crime in connection with statistical models. They also present specific examples of real-world applications such as the case of the Los Angeles Police Department. This police department employed earthquake-like models aiming to prevent crime by sending police patrols to geographical areas where models indicated that crimes were more likely to occur. Another striking example is the inference of the network topology of street gangs via agent-based simulations, in which it is quite impressive to see how this simple model agrees with the empirical data.
I totally agree with the authors when they mention that methods from statistical physics can provide direct sociological implications for crime-related problems. But, in order to reach these implications, physicists need to move further away from the “comfort zone” I previously mentioned. Contrary to what occurs, for example, in materials science, there is no “social engineer” who will be responsible for implementing models and tools that we need for a better control over the criminal activities. It seems that, although this task requires skills from both science and computing (a rare combination, even today ), statistical physicists may represent the ideal professional to take on this challenge.
 J.Q. Wilson, G.L. Kelling, Broken windows, Atl Mon, 249 (1982), pp. 29–38
 United Nations, Department of Economic and Social Affairs, Population Division, 2014. World urbanization prospects: the 2014 revision, highlights (ST/ESA/SER.A/352).
 M.R. D’Orsogna, M. Perc, Statistical physics of crime: a review, Phys Life Rev (2015) http://dx.doi.org/10.1016/j.plrev.2014.11.001 [ in this issue]
 C.A. Mattmann, Computing: a vision for data science, Nature, 493 (2012), pp. 473–475