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>> Publications at DIEP
DIEP aims at performing groundbreaking interdisciplinary research that connects different fields and shines light on aspects of emergence. Below you find a list of publications of some of the researchers associated with DIEP in 2024 and 2025. To access older publications starting in late 2020, you can check the publication archives.
>> Effective dimensional reduction of complex systems based on tensor networks
by Wout Merbis, Madelon Geurts, Clélia de Mulatier, Philippe Corboz | April 2025
The exact treatment of Markovian models of complex systems requires knowledge of probability distributions exponentially large in the number of components n. Mean-field approximations provide an effective reduction in complexity of the models, requiring only a number of phase space variables polynomial in system size. However, this comes at the cost of losing accuracy close to critical points in the systems dynamics and an inability to capture correlations in the system. In this work, we introduce a tunable approximation scheme for Markovian spreading models on networks based on matrix product states (MPSs). By controlling the bond dimensions of the MPS, we can investigate the effective dimensionality needed to accurately represent the exact 2n dimensional steady-state distribution. We introduce the entanglement entropy as a measure of the compressibility of the system and find that it peaks just after the phase transition on the disordered side, in line with the intuition that more complex states are at the 'edge of chaos'. We compare the accuracy of the MPS with exact methods on different types of small random networks and with Markov chain Monte Carlo methods for a simplified version of the railway network of the Netherlands with 55 nodes. The MPS provides a systematic way to tune the accuracy of the approximation by reducing the dimensionality of the systems state vector, leading to an improvement over second-order mean-field approximations for sufficiently large bond dimensions.
>> Mereological approach to higher-order structure in complex systems: From macro to micro with Möbius
by Abel Jansma | April 2025
Relating macroscopic observables to microscopic interactions is a central challenge in the study of complex systems. While current approaches often focus on pairwise interactions, a complete understanding requires going beyond these to capture the full range of possible interactions. We present a unified mathematical formalism, based on the Möbius inversion theorem, that reveals how different decompositions of a system into parts lead to different, but equally valid, microscopic theories. By providing an exact bridge between microscopic and macroscopic descriptions, this framework demonstrates that many existing notions of interaction, from epistasis in genetics and many-body couplings in physics, to synergy in game theory and artificial intelligence, naturally and uniquely arise from particular choices of system decomposition, or mereology. By revealing the common mathematical structure underlying seemingly disparate phenomena, our paper highlights how the choice of decomposition fundamentally determines the nature of the resulting interactions. We discuss how this unifying perspective can facilitate the transfer of insights across domains, guide the selection of appropriate system decompositions, and enable the search for new notions of interaction. To illustrate the latter in practice, we decompose the Kullback-Leibler divergence, and show that our method correctly identifies which variables are responsible for the divergence. In addition, we use Rota's Galois connection theorem to describe coarse grainings of mereologies, and efficiently derive the renormalized couplings of a 1D Ising model. Our results suggest that the Möbius inversion theorem provides a powerful and practical lens for understanding the emergence of complex behavior from the interplay of microscopic parts, with applications across a wide range of disciplines.
>> Decomposing Interventional Causality into Synergistic, Redundant, and Unique Components
by Abel Jansma | January 2025
We introduce a novel framework for decomposing interventional causal effects into synergistic, redundant, and unique components, building on the intuition of Partial Information Decomposition (PID) and the principle of Möbius inversion. While recent work has explored a similar decomposition of an observational measure, we argue that a proper causal decomposition must be interventional in nature. We develop a mathematical approach that systematically quantifies how causal power is distributed among variables in a system, using a recently derived closed-form expression for the Möbius function of the redundancy lattice. The formalism is then illustrated by decomposing the causal power in logic gates, cellular automata, and chemical reaction networks. Our results reveal how the distribution of causal power can be context- and parameter-dependent. This decomposition provides new insights into complex systems by revealing how causal influences are shared and combined among multiple variables, with potential applications ranging from attribution of responsibility in legal or AI systems, to the analysis of biological networks or climate models.
>> Field theories and quantum methods for stochastic reaction-diffusion systems
by Mauricio J. del Razo, Tommaso Lamma, Wout Merbis | September 2024
Complex systems are composed of many particles or agents that move and interact with one another. The underlying mathematical framework to model many of these systems must incorporate the spatial transport of particles and their interactions, as well as changes to their copy numbers, all of which can be formulated in terms of stochastic reaction-diffusion processes. The probabilistic representation of these processes is complex because of combinatorial aspects arising due to nonlinear interactions and varying particle numbers. This review presents the main field theory representations of stochastic reaction-diffusion systems, which handle these issues `under-the-hood'. First, we focus on bringing techniques familiar to theoretical physicists -- such as second quantization, Fock space, and path integrals -- back into the classical domain of reaction-diffusion systems. We demonstrate how various field theory representations can all be unified under a single basis-independent representation. We then extend existing quantum-based methods and notation to work directly on the level of the unifying representation, and we illustrate how they can be used to consistently obtain previous known results, such as numerical discretizations and relations between model parameters at multiple scales. Throughout the work, we contextualize how these representations mirror well-known models of chemical physics depending on their spatial resolution, as well as the corresponding macroscopic limits. The framework presented here may find applications in a diverse set of scientific fields, including physical chemistry, theoretical ecology, epidemiology, game theory and socio-economical models of complex systems. The presentation is done in a self-contained educational and unifying manner such that it can be followed by researchers across several fields.
>> Time, Spacetime and F-Theory
by Enrico Cinti, Marco Sanchioni | August 2024
This Chapter explores the philosophical and ontological implications of F-theory, a non-perturbative extension of Type IIB string theory, mainly focusing on the apparent existence of two temporal dimensions. The paper proposes an interpretation that advocates for a single temporal dimension grounded in a brane-based ontology, challenging the conventional understanding of time and spacetime in F-theory. Moreover, it discusses the implications of a brane-based ontology for spacetime emergence, providing a novel understanding of the relations between spatiotemporal and non-spatiotemporal structures.
>> Anchoring as a Structural Bias of Deliberation
by Sebastian Till Braun, Soroush Rafiee Rad, Olivier Roy | July 2024
We study the anchoring effect in a computational model of group deliberation on preference rankings. Anchoring is a form of path-dependence through which the opinions of those who speak early have a stronger influence on the outcome of deliberation than the opinions of those who speak later. We show that anchoring can occur even among fully rational agents. We then compare the respective effects of anchoring and three other determinants of the deliberative outcome: the relative weight or social influence of the speakers, the popularity of a given speaker’s opinion, and the homogeneity of the group. We find that, on average, anchoring has the strongest effect among these. We finally show that anchoring is often correlated with increases in proximity to single-plateauedness. We conclude that anchoring can constitute a structural bias that might hinder some of the otherwise positive effects of group deliberation
>> Reassessing the alternative ecosystem states proposition in the African savanna-forest domain
by Steven I. Higgins, Swarnendu Banerjee, Mara Baudena, David M. J. S. Bowman, Timo Conradi, Pierre Couteron, Laurence M. Kruger, Robert B. O'Hara, Grant J. Williamson | July 2024
Ecologists are being challenged to predict how ecosystems will respond to climate changes. According to the Multi-Colored World (MCW) hypothesis, climate impacts may not manifest because consumers such as fire and herbivory can override the influence of climate on ecosystem state. One MCW interpretation is that climate determinism fails because alternative ecosystem states (AES) are possible at some locations in climate space. We evaluated theoretical and empirical evidence for the proposition that forest and savanna are AES in Africa. We found that maps which infer where AES zones are located were contradictory. Moreover, data from longitudinal and experimental studies provide inconclusive evidence for AES. That is, although the forest-savanna AES proposition is theoretically sound, the existing evidence is not yet convincing. We conclude by making the case that the AES proposition has such fundamental consequences for designing management actions to mitigate and adapt to climate change in the savanna-forest domain that it needs a more robust evidence base before it is used to prescribe management actions.
>> Operator Entanglement Growth Quantifies Complexity of Cellular Automata
by Calvin Bakker, Wout Merbis | June 2024
Cellular automata (CA) exemplify systems where simple local interaction rules can lead to intricate and complex emergent phenomena at large scales. The various types of dynamical behavior of CA are usually categorized empirically into Wolfram’s complexity classes. Here, we propose a quantitative measure, rooted in quantum information theory, to categorize the complexity of classical deterministic cellular automata. Specifically, we construct a Matrix Product Operator (MPO) of the transition matrix on the space of all possible CA configurations. We find that the growth of entropy of the singular value spectrum of the MPO reveals the complexity of the CA and can be used to characterize its dynamical behavior. This measure defines the concept of operator entanglement entropy for CA, demonstrating that quantum information measures can be meaningfully applied to classical deterministic systems.
>> New asymptotically (Anti)-de Sitter black holes in (super)gravity
by Jay Armas, Gianbattista-Piero Nicosia | June 2024
We use the duality between gravitational dynamics and fluids living on dynamical surfaces carrying multiple charges, known as the blackfold approach, to perturbativaly construct new asymptotically global (Anti)-de Sitter multi-spinning, non-extremal, multi-charged black holes in theories of higher-dimensional gravity minimally coupled to a dilaton and higher-form gauge fields in spacetime dimensions D≥5, and new asymptotically AdSl×Sm black holes in type IIB and eleven-dimensional supergravity. These solutions include the generalisation of the Kerr-Newman solution to (A)dS carrying either electric or string charge, generalisations of black rings to higher-dimensions with 𝕊p×𝕊n+1 horizon topology, static de Sitter solutions carrying arbitrary q-brane charge, as well as various asymptotically AdSl×Sm multi-charged and multi-spinning black hole solutions, some of which correspond to novel thermal states in N=4 Super-Yang-Mills theory
>> Fractonic solids
by Akash Jain | June 2024
Fractons are exotic quasiparticles whose mobility in space is restricted by symmetries. In potential real-world realisations, fractons are likely lodged to a physical material rather than absolute space. Motivated by this, we propose and explore a new symmetry principle that restricts the motion of fractons relative to a physical solid. Unlike models with restricted mobility in absolute space, these fractonic solids admit gauge-invariant momentum density, are compatible with boost symmetry, and can consistently be coupled to gravity. We also propose a holographic model for fractonic solids.
>> Enriched Quantales Arising from Complete Orthomodular Lattices
by Soroush Rafiee, Joshua Sack, Shengyang Zhong | June 2024
This paper connects complete orthomodular lattices to two enriched quantale structures. Complete orthomodular lattices emphasize a static perspective of a quantum system, helping us reason about testable properties of a quantum system. Quantales offer a dynamic perspective, helping us reason about the structure of quantum actions. We enrich quantales with an orthocomplementation-inducing operator, and call these structures orthomodular dynamic algebras. One type of orthomodular dynamic algebra distinguishes the joins of any two different sets of atoms, while the other distinguishes elements by the collective behavior of the atoms below it. We show that both orthomodular dynamic algebras are unital, and the unit is the top element of an induced orthomodular lattice. We provide a categorical equivalence between both orthomodular dynamic algebras and complete orthomodular lattices with isomorphisms, and we show that this equivalence is preserved when augmenting the orthomodular dynamic algebras with an involution. These equivalences help clarify the relationship between static and dynamic quantum structures.
>> Beyond the Quantum Membrane Paradigm: A Philosophical Analysis of the Structure of Black Holes in Full QG
by Enrico Cinti, Marco Sanchioni | June 2024
This paper presents a philosophical analysis of the structure of black holes, focusing on the event horizon and its fundamental status. While black holes have been at the centre of countless paradoxes arising from the attempt to merge quantum mechanics and general relativity, recent experimental discoveries have emphasised their importance as objects for the development of Quantum Gravity. In particular, the statistical mechanical underpinning of black hole thermodynamics has been a central research topic. The Quantum Membrane Paradigm, proposed by Wallace (Stud Hist Philos Sci Part B 66:103-117, 2019), posits a real membrane made of black hole microstates at the black hole horizon to provide a statistical mechanical understanding of black hole thermodynamics from an exterior observer’s point of view. However, we argue that the Quantum Membrane Paradigm is limited to low-energy Quantum Gravity and needs to be modified to avoid reference to geometric notions, such as the event horizon, which presumably do not make sense in the non-spatiotemporal context of full Quantum Gravity. Our proposal relies on the central dogma of black hole physics. It considers recent developments, such as replica wormholes and entanglement wedge reconstruction, to provide a new framework for understanding the nature of black hole horizons in full Quantum Gravity.
>> Odd viscous flow past a sphere at low but nonzero Reynolds numbers
by Ruben Lier | May 2024
Measuring lift force on symmetrically shaped obstacles immersed in laminar flow is the quintessential way of signalling odd viscosity. For flow past cylinders, such a lift force does not arise when incompressibility and no-slip boundary conditions hold, whereas for spheres, a lift force was found in Stokes flow, applying to cases where the Reynolds number is negligible and convection can be ignored. When considering the role of convection at low but nonzero Reynolds numbers, two arising hurdles are the Whitehead paradox and the breaking of axial symmetry, which are overcome by asymptotic matching and the Lorentz reciprocal theorem respectively. We also consider the case where axial symmetry is retained because the translation of the sphere is aligned with the anisotropy vector of odd viscosity. We find that while lift vanishes, the interplay between odd viscosity and convection gives rise to a stream-induced non-vanishing torque.
>> Hydrodynamics of thermal active matter
by Jay Armas, Akash Jain, Ruben Lier | May 2024
Active matter concerns many-body systems comprised of living or self-driven agents that collectively exhibit macroscopic phenomena distinct from conventional passive matter. Using Schwinger-Keldysh effective field theory, we develop a novel hydrodynamic framework for thermal active matter that accounts for local temperature variations and the ensuing stochastic effects. This framework provides a deeper understanding of energy balance, second law of thermodynamics, and thermostated steady states in active matter, while also addressing the systematic violations of fluctuation-dissipation theorem and detailed balance. We use our framework of active hydrodynamics to develop effective field theory actions for active superfluids and active nematics that offer a first-principle derivation of various active transport coefficients and feature activity-induced phase transitions.
>> Duality, Underdetermination, and the Uncommon Common Core
by Daniel Grimmer, Enrico Cinti, Rasmus Jaksland| March 2024
Dualities arise when two seemingly different descriptions of the world are physically equivalent, suggesting that either description can be used to describe a given system. This raises the question of which description, if any, is true and raises worries of empirical underdetermination. This paper explores the underdetermination problem in the context of dualities and focuses on the viability of a common core ontology as a solution. The common core suggests that one should only ontologically commit to what is invariant under the duality map between the dual descriptions. The paper examines this solution through the lens of Fourier duality in non-relativistic quantum mechanics and raises con- cerns about the existence and adequacy of the common core. It argues that the common core might not be ontologically rich enough to support a genuine realist commitment and questions whether it should be preferred over the dual descriptions. By doing so, the analysis highlights the challenges of employing the common core interpretation in quan- tum mechanics and also in other dualities such as T-duality and AdS/CFT, especially for purposes of breaking underdetermination. Dualities are, we conclude, likely examples
of underdetermination and therefore a challenge to scientific realism.
>> SUSY, Spin-Statistics, and all that... On the contrast between Spin-Statistics and Wigner’s Theorem
by Enrico Cinti, Marco Sanchioni| March 2024
Supersymmetry is a conjectured symmetry that relates standard model's bosons and
fermions. The spin-statistics theorem, which states that a particle's statistics depends on its spin, is a crucial component of quantum field theory's analysis of matter. Prima facie, supersymmetry creates problems for the theoretical structure underpinned by the spin-statistics theorem. Since supersymmetry relates bosons and fermions, the distinction between particles obeying Bose-Einstein or Fermi-Dirac statistics seems to collapse since, ultimately, they are part of a single supermultiplet, that is, the actual degree of freedom of supersymmetric quantum field theory. This article aims to evaluate the status of the spin- statistics theorem within supersymmetric quantum field theories and which strategies one can implement to make sense of this state of affairs. In particular, we argue that there are two main options in the face of the conflict between Wigner's theorem and the spin-statistics theorem: either we abandon the validity of the spin-statistics theorem and adopt an invariant superfield ontology, or we abandon Wigner's theorem and uphold spin-statistics theorem, at the price, however, of introducing a significant redundancy in our ontological. Moreover, we explore how these two options relate to important philosophical debates, such as the nature of superspace and spacetime ontologies, and the debates between motivationalists and interpretationalist regarding physical symmetry.
>> Higher-group global symmetry and the bosonic M5 brane
by Jay Armas, Giorgos Batzios, Akash Jain| February 2024
Higher-group symmetries are combinations of higher-form symmetries which appear in various field theories. In this paper, we explain how higher-group symmetries arise in 10d and 11d supergravities when the latter are coupled to brane sources. Motivated by this observation, we study field theories at zero and finite temperature invariant under a class of continuous Abelian higher-group symmetries. We restrict the analysis to the low-energy regime where the dynamical field content exclusively consists of Goldstone fields arising from the spontaneous breaking of higher-group and spacetime symmetries. Invariant quantities are constructed and the phases of matter are classified according to the pattern of spontaneous symmetry breaking. With respect to supergravity, we highlight how such Goldstone effective theories provide a symmetry-based interpretation for the theories living on D/M-branes. As an explicit example we construct a 6-group invariant action for the bosonic M5 brane, consistent with the self-duality of the 3-form field strength on the brane. While the self-duality condition in the bosonic case needs to be imposed externally as a constraint at zero temperature, we find an equilibrium effective action for the bosonic M5 brane at finite temperature that inherently implements self-duality.
>> Holographic transport in anisotropic plasmas
We study energy-momentum and charge transport in strongly interacting holographic quantum field theories in an anisotropic thermal state by contrasting three different holographic methods to compute transport coefficients: standard holographic calculation of retarded Greens functions, a method based on the null-focusing equation near horizon and the novel method based on background variations. Employing these methods we compute anisotropic shear and bulk viscosities and conductivities with anisotropy induced externally, for example by an external magnetic field. We show that all three methods yield consistent results. The novel method allows us to read off the transport coefficients from the horizon data and express them in analytic form from which we derive universal relations among them. Furthermore we extend the method based on the null-focusing equation to Gauss-Bonnet theory to compute higher derivative corrections to the aforementioned transport coefficients.
>> Slip-induced odd viscous flow past a cylinder
Ruben Lier | February 2024
Odd viscosity is a transport coefficient that can occur when fluids experience breaking of parity and time-reversal symmetry. Previous knowledge indicates that cylinders in incompressible odd viscous fluids, under no-slip boundary conditions, do not exhibit lift force, a phenomenon that poses challenges for the experimental detection of odd viscosity. This study investigates the impact of slip in Stokes flow, employing the odd generalization of the Lorentz reciprocal theorem. Our findings reveal that, at linear order in slip length, lift does not manifest. Subsequently, we explore the scenario involving a thin sheet with momentum decay as well as that of a finite system size, demonstrating that for Stokes flow lift does occur for the second order slip length contribution. We address cylinder flow beyond the Stokes approximation by solving the Oseen equation to obtain a fluid profile that shows an interplay between odd viscosity and inertia, and acquire an explicit expression for the leading order slip length contribution to Oseen lift at low Reynolds number.
>> Dipole superfluid hydrodynamics II
Akash Jain, Kristan Jensen, Ruochuan Liu, Eric Mefford| January 2024
We present a dissipative hydrodynamic theory of "s-wave dipole superfluids" that arise in phases of translation-invariant and dipole-symmetric models in which the U(1) symmetry is spontaneously broken. The hydrodynamic description is subtle on account of an analogue of dangerously irrelevant operators, which requires us to formalize an entirely new derivative counting scheme suitable for these fluids. We use our hydrodynamic model to investigate the linearized response of such a fluid, characterized by sound modes ω∼±k−ik2, shear modes ω∼−ik2, and magnon-like propagating modes ω∼±k2−ik4 that are the dipole-invariant version of superfluid "second sound" modes. We find that these fluids can also admit equilibrium states with "dipole superflow" that resemble a polarized medium. Finally, we couple our theory to slowly varying background fields, which allows us to compute response functions of hydrodynamic operators and Kubo formulas for hydrodynamic transport coefficients.
>> Asymmetric games on networks: mapping to Ising models and bounded rationality
Filippo Zimmaro, Serge Galam, Marco Alberto Javarone | January 2024
We investigate the dynamics of coordination and consensus in an agent population. Considering agents endowed with bounded rationality, we study asymmetric coordination games using a mapping to random field Ising models. In doing so, we investigate the relationship between group coordination and agent rationality. Analytical calculations and numerical simulations of the proposed model lead to novel insight into opinion dynamics. For instance, we find that bounded rationality and preference intensity can determine a series of possible scenarios with different levels of opinion polarization. To conclude, we deem our investigation opens a new avenue for studying game dynamics through methods of statistical physics.
>> Topological plasma oscillations in the solar tachocline
Ruben Lier, Richard Green, Jan de Boer, Jay Armas | January 2024
We study the properties of plasma oscillations in the solar tachocline using shallow-water magnetohydrodynamic equations. These oscillations are expected to correlate with solar activity. We find new qualitative features in the equatorial spectrum of magnetohydrodynamic oscillations associated with magneto-Rossby and magneto-Yanai waves. By studying this spectrum in terms of band theory, we find that magneto-Kelvin and magneto-Yanai waves are topologically protected. This highlights the important role of these two classes of waves, as robust features of the plasma oscillation spectrum, in the interpretation of helioseismological observations.
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