Emergence of Hydrodynamics: from extreme matter to the early universe and society
​​​Welcome to the EAAS workpackage 2! Here you will find short accessible descriptions of the scientific papers that have been published in the context of this EAAS workpackage. If something catches your interest, feel free to click the links to explore further!
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What is this workpackage about?
Emergence is how simple parts can come together to create complex, large-scale behaviour. A powerful tool for understanding this is hydrodynamics—a theory originally developed to describe how fluids like water or air flow. Surprisingly, it has been discovered that the same ideas can be used to describe many different kinds of systems, far beyond liquids. Hydrodynamics can help us understand how groups behave as a whole, no matter what they are made of. These groups could consist of particles, cells, bacteria, or even people. In other words, it provides a kind of “universal language” for studying collective behaviour across very different situations and scales.
In this workpackage, we explore both how this approach works and where its limits might be. We also apply it to a wide range of topics: from extreme forms of matter in the universe, such as those found just after the Big Bang or inside neutron stars, to patterns that emerge in human societies, like social segregation. By connecting these very different systems, we aim to better understand the common principles that shape complex behaviour in our world.
The Laws Governing the Growth of Cities
​​By: Wout Merbis, Fernando A.N. Santos, Jay Armas, Frank Pijpers and Mike Lees [arXiv:2604.01969]
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Cities are not just collections of buildings and roads; they are living systems that grow in patterned ways. For decades, researchers have found that many urban quantities follow “scaling laws”: when a city becomes larger, things like infrastructure, land use, innovation, wealth, and even crime do not simply increase one-to-one, but often change in systematic nonlinear ways. At the same time, cities are not spatially uniform. People cluster in neighborhoods, corridors, and centers, giving cities a fractal-like structure across scales. Our paper asks how this internal spatial organization relates to the broader scaling laws of urban science. Using high-resolution population maps for cities in the Netherlands and around the world, we study not only how population is distributed across space, but also how strongly it fluctuates from one place to another within the same city.
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The central finding is that two seemingly different properties of cities are tightly linked. One exponent describes urban form: how the average population contained in an area changes as we zoom out to larger spatial scales. The other describes fluctuations: how uneven or variable the population becomes across those same scales. Across hundreds of cities and many decades, these two exponents do not vary independently, but instead fall close to a line. In other words, the shape of a city and the intensity of its internal population variation are connected by a common scaling relation. This relation is robust, but not universal: it differs somewhat across continents and changes over time, suggesting that urban development follows common principles while still reflecting geography, planning traditions, and historical growth paths.​
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​​​Fig. 1: Multiscale analysis for the city of Amsterdam. Population data is aggregated into grid cells of increasing size and the mean and variance of each is computed at each grid size, leading to the exponents for urban form and population fluctuations.
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This has important implications for urban scaling research. Classical urban scaling theory often focuses on whole-city totals, such as how GDP or infrastructure scale with total population. Our results show that these aggregate outcomes are likely constrained by a city’s internal spatial structure. If two cities have the same population size but one is more spatially correlated—meaning that dense and sparse areas are organized in a more strongly patterned way—it may also have a different baseline capacity for social interaction, mobility, inequality, or economic productivity. In that sense, variation in urban scaling exponents across cities may not just be statistical noise or a problem of measurement, but a reflection of real differences in how urban populations are organized in space. This helps explain why urban scaling laws are often systematic but not perfectly universal.
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More broadly, the paper suggests that understanding cities requires linking urban form and urban function more closely. Population maps are not just descriptive background data; they contain information about the multiscale organization of cities that may shape downstream outcomes relevant to planning and policy. Because many important urban indicators depend on local concentration and variation, the scaling relation we identify can serve as a constraint for urban growth models and as a guide for studying inequality, infrastructure demand, and socio-economic performance. In this way, the work adds a new layer to urban scaling theory: it shows that the way people are distributed within cities helps determine how cities behave as they grow.
How the Primordial Soup Spins
Ordinary matter is built from protons and neutrons, and those in turn are made of smaller particles called quarks, held together by gluons. Under normal conditions, quarks and gluons are never seen wandering around freely. But in the first microseconds after the Big Bang, the Universe was so hot and dense that they were not locked inside protons and neutrons at all: they formed a different state of matter called the quark–gluon plasma. Today, physicists briefly recreate that same state by colliding heavy atomic nuclei at enormous energies at facilities such as RHIC in the US and the LHC at CERN. What forms is a tiny fireball that exists for only an instant before cooling back into ordinary particles. Surprisingly, experiments have shown that this “primordial soup” behaves less like a gas and more like an almost perfect liquid.
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That is why the quark–gluon plasma matters so much. It gives scientists a way to study the strong force—the force that binds the building blocks of atomic nuclei—under the most extreme conditions we can create in the laboratory. It also offers a window onto how the early Universe evolved from a hot soup of elementary particles into the matter we know today. In other words, by studying this tiny, short-lived droplet, researchers are learning both about the deepest laws of nature and about the history of the cosmos.
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One of the most exciting discoveries in this field is that the plasma does not just flow—it can also rotate. When two heavy nuclei collide slightly off-center rather than head-on, the collision carries a huge amount of angular momentum. Part of that angular momentum can end up in the hot plasma as a kind of microscopic whirlpool, or vorticity. Physicists cannot look directly inside the plasma while it exists, so they infer this rotation from the particles that come out afterward. A key breakthrough came when the STAR experiment found that certain particles called Lambda hyperons emerged with their spins slightly aligned with the overall angular momentum of the collision. Because Lambda hyperons decay in a way that reveals their spin direction, they act as tiny built-in compasses. That result gave the first direct evidence that the quark–gluon plasma is an extraordinarily vortical, swirling fluid.
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This is where spin hydrodynamics enters the story. Hydrodynamics is the theory physicists use to describe the collective flow of fluids. It already works remarkably well for the quark–gluon plasma. But once experiments began to detect spin polarization, ordinary hydrodynamics was no longer enough. Scientists needed a theory that could describe not only how the plasma flows, but also how that flow is tied to the quantum angular momentum of the particles inside it. Spin hydrodynamics is that extended framework: it tracks how bulk rotation, local fluid motion and particle spin influence one another. That makes it essential if we want to turn tiny polarization signals into real information about what the plasma was doing internally.
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The relevance of this work done within EAAS is that it tackles a basic theory problem in spin hydrodynamics and shows how to formulate the theory so that the usual rules of thermodynamics still work. The authors also work out concrete examples for simple quantum fields, helping connect abstract equations to measurable quantities. In plain language, the paper helps build a reliable dictionary for spin hydrodynamics: how to match a microscopic understanding of spin fluids with a macroscopic description of the collective phenomena– the central problem of Emergence. In other words, the paper is building the translation manual between what detectors see and what the spinning primordial soup was actually doing.
Equal Preferences, Unequal Outcomes: How One Group Comes to Dominate the City
​​Cities can become segregated even when people do not have a strong preference to live among their own kind. This puzzling effect was famously shown by the economist Thomas Schelling, who demonstrated that mild individual preferences can still produce sharply divided neighborhoods.
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In this work, we revisit that question from a new angle and uncover a surprising result: even when two groups have exactly the same preferences, one group can suddenly come to dominate a city.
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Instead of assuming that people consciously optimize their happiness or follow strict rules about when to move, we model residential change as a stochastic process, similar to chemical reactions. People move in or out of neighborhoods at certain rates, influenced by who already lives nearby, but without making deliberate “best” decisions. Vacant homes play an essential role by enabling movement, much like empty seats in a game of musical chairs.
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Using this framework, we find three key behaviors:
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Mixed neighborhoods where different groups are well integrated.
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Segregated neighborhoods where people cluster with similar neighbors, but both groups remain equally represented overall.
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A tipping point where, beyond a critical strength of in-group attraction, the city suddenly shifts to a state where one group dominates, even though both groups follow identical rules.
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​​​This tipping point behaves much like phase transitions in physics, similar to how a magnet suddenly becomes magnetized when cooled below a critical temperature. However, careful analysis shows that this transition does not fit neatly into any well-known physical universality class, suggesting genuinely new collective behavior.
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The broader message is important for urban policy and social science: both large-scale segregation and neighborhood tipping into a dominance of one type can emerge from simple and symmetric rules between individuals.
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Because our model is based on measurable movement rates rather than hidden personal preferences, it also opens the door to closer connections with real housing and mobility data. This makes it a promising framework for understanding, and possibly anticipating, sudden shifts in urban demographics.