# IV National Meeting of Statistical Physics

# Resumos das palestras convidadas

## Dhar Deepack

Asymmetric simple exclusion process on the percolation cluster As the simplest model of transport of interacting particles in a disordered medium, we consider the asymmetric simple exclusion process in which particles with hard-core interactions perform biased random walks, on the supercritical percolation cluster. In this process, the long time trajectory of a marked particle consists of steps on the backbone, punctuated by time spent in side-branches. We study the probability distribution in the steady state of the waiting time TW of a randomly chosen particle, in a side-branch since its last step along the backbone. We argue that for large fields, the probability distribution of log TW has multiple well separated peaks. The fractional number of particles that have been in the same side-branch for a time interval greater than TW decreases more slowly than any power law, as exp (−c√log T W ) for arge T W , where c depends only on the bias field. However, these long timescales are not reflected in the eigenvalue spectrum of the Markov evolution matrix. The same slow decay is also seen in the velocity -velocity autocorrelation function of a tagged particle.

## Hans Herrmann

Criticality of the Brain Dept. de Física, UFC, Fortaleza & PMMH, ESPCI Paris The activity of the resting state of the brain exhibits avalanches of spiking activity of sizes that follow a power-law distribution. I will present Monte Carlo simulations of self-organized and driven models that do reproduce avalanches fulfilling the scaling laws of a general theory for crackling noise. The power spectrum, however, does not agree with this theory. We explain this deviation by establishing a phase diagram involving the fraction of inhibitory neurons and finding that the brain operates at a certain distance from the critical point. In an alternative attempt to grasp brain criticality we investigate the spiking patterns of model generated data as well as in vitro and in vivo neural systems mapping them to a fully connected Ising model with local fields and interaction constants which are obtained by a Boltzmann machine. The distributions of these fields and interaction constants seem to be universal. A Monte Carlo simulation suggests that this Ising system operates at a critical point separating a ferromagnetic from a paramagnetic phase. Finally we will assess the learning capacity of our neural network model by training various logical functions finding scaling laws in the strength of synaptic adaptation and observing memory loss while learning several functions simultaneously.

## Cristina Masoller

New indicators for early detection of critical transitions Complex systems often exhibit abrupt and dangerous regime transitions. Anticipating these changes can be crucial to implementing adaptation measures. So far, many data-driven indicators of upcoming bifur- cations and regime changes have been proposed. However, their performance depends on the characteristics of the analyzed system and the characteristics of the observed data. In this talk, I will discuss the performance of classical and new early warning indicators, using real-world data (vegetation images to identify desertification transitions), as well as experimental data generated with controlled variation of the bifurcation parameter.

## Angelica Sousa da Mata

Complex networks applied to neuroscience and QI* Complex networks can be used in different contexts whose objective is to investigate a set of elements that interact with each other. In this talk, we will show two interesting applications of complex networks, the first application is associated with the study of brain networks and the second one is related to the propagation of quantum information. In the first one we use real data from brain networks, obtained by magnetic resonance imaging, of more than 1000 young adults and 700 healthy elderly people, provided by the Human Connectome project. The objective was to investigate network centrality measures such as cluster coefficient and different measures of entropy such as geodesic entropy and von Newmann entropy to analyze the behavior of the human brain throughout aging and differences between genders. In the second case, we know that the quantum internet can be modeled by a network of locations interconnected by quantum channels. We will use preferential connection networks that take into account the Euclidean distance between the elements of the system to model the connection of optical fibers and verify how the photon transmission network behaves on this substrate, in comparison with substrates already used in the literature.

## Ricardo Luiz Viana

Shadowability breakdown of chaotic orbits in coupled systems Autores: Bruno M. Czajkowski and Ricardo L. Viana Abstract: Metric properties of invariant chaotic sets, like chaotic attractors, are closely related to the structure of the unstable periodic orbits embedded in this set. As a system parameter is varied through a critical value, a chaotic attractor lying on an invariant subspace may become transversely unstable, undergoing a blowout bifurcation. We use periodic orbit theory to investigate some of the properties of the blowout bifurcation for two systems of coupled chaotic having a synchronized state, one being a discrete-time mapping [1], and another a continuous-type Lorenz-like system [2]. We also study riddling of basins associated with chaotic synchronization for these systems with the help of periodic orbit theory and a biased stochastic model that uses the properties of the finite-time Lyapunov exponents. The severe breakdown of shadowability of chaotic trajectories due to unstable dimension variability and its relation with the blowout bifurcation are discussed. [1] B. M. Czajkowski and R. L. Viana, Chaos, Solitons and Fractals, 184 (2024) 114994 [2] B. M. Czajkowski and R. L. Viana, Chaos, 31 (2024) 093113

## Leticia Ribeiro de Paiva

Emergent phases in termite groups Active matter can be dened as systems made of a large number of interacting constituents able to convert some source of energy into directed motion [1]. Despite being self-propelled, these constituents are interconnected in such a way that they move synchronically. In doing so, collective behavior emerges spontaneously. Termite groups can be readily spotted as biological active matter. They form groups of interacting individuals, and such interactions result in collective behaviors which translate into temporal and spatial emergent patterns [2-5]. Here we inspect the dierent spatial patterns that have emerged in termites kept in closed arenas [5]. We identify disordered, clustering and milling phases or spatial patterns. We parameterize these termite phases and their transitions, aiming to oer renements in the understanding of these aspects of self-propelled particles in active matter both in living and articial systems where close-range contacts are important. References [1] E. Fodor and M. C. Marchetti. The statistical physics of active matter: From self-catalytic colloids to living cells. Physica A, 504:106{120, 2018. [2] O. Miramontes and O. DeSouza. The nonlinear dynamics of survival and social facilitation in termites. Journal of Theoretical Biology, 181(4):373{ 380, 1996. [3] O. Miramontes, O. DeSouza, L. R. Paiva, A. Marins, and S. Orozco. Levy Flights and Self- Similar Exploratory Behaviour of TermiteWorkers: Beyond Model Fitting. PLoS ONE, 9(10):e111183, oct 2014. [4] L. R. Paiva, A. Marins, P. Cristaldo, D. Ribeiro, S.G. Alves, A. Reynolds, O. DeSouza, and O. Miramontes. Scale-free movement patterns in termites emerge from social interactions and preferential attachments. PNAS, 118(20):e2004369118, 2021. [5] L. R. Paiva, S. G. Alves, O. DeSouza, O. Miramontes. Emergent dynamical phases and collec-tive motion in termites. in preparation. The authors thank FAPEMIG for the nancial support.

## Carlos Eduardo Fiore dos Santos

Non-equilibrium thermodynamics of collective heat engines We introduce a class of stochastic engines in which the regime of units operating synchronously can boost the performance. Our approach encompasses a minimal setup composed of 𝑁 interacting units placed in contact with two thermal baths and subjected to a constant driving worksource. The interplay between unit synchronization and interaction leads to an efficiency at maximum powers and maximum efficiencies, above all they close to each other for a broad set of parameters. We also uncover a new phenomena about them, in which order-disorder (collective-independent) phase transitions split into two different transition points and classifications are also different. Our results depict novel insights into heat engines and phase transitions under nonequilibrium conditions.

## Márcia C. Barbosa

Anomalous behaviors of nanoconfined water Marcia C. Barbosa and Fernanda Leivas Water exhibits over 70 anomalous behaviors, many of which are present in everyday life. In this talk we show how we can explain these anomalies in a simple way with a two-scale effective potential representing molecules that bind or do not bind by hydrogen bonds. This two-scale concept together with the hydrophilicity and hydrophobicity properties of water is used to suggest a mechanism for water capture at the nanoscale. This procedure identified by molecular dynamics simulations is experimentally identified as viable.

## Felix Sharipov

Direct Simulation Monte Carlo method The Boltzmann equation is the master equation to describe non-equilibrium processes in dilute rarefied gases on the mesoscopic level. The direct simulation Monte Carlo (DSMC) is a probabilistic method to solve the Boltzmann equation. The main idea of this method is a consideration of a huge number of model particles simulating the interaction between them and their interaction with surfaces. The number of intermolecular collisions is calculated via the real collision frequency and statistical weight of each model particles. The gas-surface interaction is modelled by a specific scattering kernel. Finally, the macroscopic haracteristics such as density, bulk velocity and temperature, are calculated as average values of microscopic quantities. Since the number of particles is restricted, the statistical scattering of macroscopic characteristics is significant. To reduce this scattering to reasonable values, a number of samples must be large enough. The DSMC method has many advantages. It is easy to apply it to complicated geometrical configuration. The CPU time is not very sensitive to many generalizations such as gaseous mixtures, polyatomic gases, molecular issociation etc. In open literature one can find numerical codes based on the DSMC method that can be directly used in practice. Some examples of applications of the method will be shown.

## Gandhi M. Viswanathan

Understanding the controversy and its resolution regarding the optimality of Levy w

## Sabrina B. Lino Araujo

Speciation under migration: insights from individual-based models Geographic isolation is a central mechanism of speciation, but perfect isolation of populations is rare. Although speciation can be hindered if gene flow is large, intermediate levels of migration can enhance speciation by introducing genetic novelty in the semi-isolated populations or founding small communities of migrants. In this talk, I will show how an individual-based model can be used to understand the speciation processes. I will focus on a two-island-neutral model with continuous and intermittent migration. Our studies show that low migration can induce an unexpected asymmetrical frequency of speciation between islands. In an intermittent scenario of migration, speciation can be favored or disfavored depending on the intensity and frequency of migration. I'll also present the macroevolutionary patterns that emerged from this system and discuss how migration's history can impact populations' phylogeny.

## Jeferson J. Arenzon

Emergent cooperative behavior in transient compartments Jeferson J. Arenzon1, 2 and Luca Peliti3 Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre RS, Brazil 2 Instituto Nacional de Ciência e Tecnologia - Sistemas Complexos, Brazil 3 Santa Marinella Research Institute, Santa Marinella (RM), Italy We discuss a minimal model of multilevel selection on structured popula-tions, considering the interplay between game theory and population dynamics. Through a bottleneck process, finite groups are formed with cooperators and defectors sampled from an infinite pool. After the fragmentation, these tran-sient compartments grow until the maximal number of individuals per compart-ment is attained. Eventually, all compartments are merged, well mixed and the whole process is repeated. We show that cooperators, even if interacting only through mean-field intra-group interactions that favor defectors, may perform well because of the inter-group competition and the size diversity among the compartments. These cycles of isolation and coalescence may therefore be im- portant in maintaining diversity among different species or strategies and may help to understand the underlying mechanisms of the scaffolding processes in the transition to multicellularity. REF.: Arenzon and Peliti, Phys. Rev. E 108 (2023) 034409

## Celia Anteneodo

Non-Markovian opinion dynamics Social interactions play a key role in opinion formation and can lead to different self-organized collective states. However, random factors are always present and can induce opinion changes independently of the interactions, hindering the ability of the social group to converge to consensus. An additional factor, termed “aging”, might significantly influence opinion dynamics. It reflects the increased resistance of individuals to change their opinion over time, such that opinion changes can become less likely the longer an agent has adopted a given opinion state. In recent research [1,2], we studied the impact of aging on standard noisy opinion models, based on mean-field analytical predictions and agent-based simulations. Notably, we observe a non-monotonic relationship between the critical value of order-disorder transition and the rate of decay of the probability of change due to aging. Optimal consensus emerges at an intermediate aging rate, highlighting the nuanced role aging plays in opinion formation. [1] Aging in some opinion formation models: a comparative study, J Llabres, S Oliver-Bonafoux, C Anteneodo, R Toral, Physics 2024, 6, 515-528 (2024) [2] Noisy kinetic-exchange opinion model with aging, AR Vieira, J Llabrés, R Toral, C Anteneodo. Physical Review E 109 (6), 064119 (2024)

## Steve Tomsovic

Controlling Many-Body Quantum Chaos: Optimal Coherent Targeting Co-authors & Affiliations: Lukas Beringer – University of Regensburg (UR) Mathias Steinhuber – UR Juan Diego Urbina – UR Klaus Richter – UR Abstract: The control and stabilization of many-body quantum systems whose classical counterparts exhibit highly chaotic motion is a challenging problem. The presence of many-body quantum chaotic dynamics is often conceptualized as the ultimate enemy of quantum device control as it leads rapidly to thermalization, and is certainly a fundamental hindrance to controlling quantum computation. However, what if chaos could be harnessed instead as a resource for quantum control just as has been shown for classical systems? One of the principal goals of controlling classically chaotic dynamical systems is known as targeting, which is the very weakly perturbative process of using the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. It relies on a kind of "inverse butterfly effect": fast exponential convergence. In this talk we develop a many-body quantum control technique inspired by classical targeting. Starting from an initial quantum state in a quantum chaotic system: “how can one transfer the chaotic many-body system to a predetermined remote target state most efficiently?’’

## Eduardo Altmann

Statistical laws: the complex systems approach to data science From power-laws in Econophysics and Complex Networks to scaling laws in Urban systems, statistical laws play a fundamental role in mutidiciplinary applications of Statistical Physics. In this talk, I will review and critically analyse the potential and limitations of the statistical-law approach to data analysis, contrasting it with the "machine-learning" approach that dominates Data Science. References: [1] E. G. Altmann, "Statistical laws in complex systems", arXiv:2407.19874 (2024) [2] J. M. Moore, G. Yan, E. G Altmann "Nonparametric Power-Law Surrogates" , Phys. Rev. X 12, 021056 (2022)

## Jan Michael Rost

The joint origin of time and temperature from a global entangled state of system and environment The reduction of necessary prerequisites in the mathematical description of nature has been a lasting motivation to evolve theory in physics. Here, we will show that time and temperature have a common root in a stationary global entangled state of a system and its environment, in other words time and temperature are not fundamental. This achieved by demonstrating how time evolution for system and environment emerges by their separation in a relational fashion leaving the global state unchanged. Based on the seminal idea by Page and Wootters [1], we formulate the extreme quantum case of relational time [2] and argue that our perception of time is consistent with its semiclassical limit. Furthermore, we will introduce relational imaginary time evolution and show that it implies the fundamental thermodynamic relation of statistical physics if the global state is maximally entangled [3], without counting of states as required even by modern approaches such as canonical typicality [4]. [1] D. N. Page and W. K. Wootters, Evolution without evolution: Dynamics described by stationary observables, Phys. Rev. D 27, 2886 (1983). [2] S. Goldstein, J. L. Lebowitz, R. Tumulka, and N. Zanghì, Canonical typicality, Phys. Rev. Lett. 96, 050403 (2006). [3] S. Gemsheim and J. M. Rost: Emergence of time from quan- tum interaction with the environment, Phys. Rev. Lett. 131, 140202, (2023). [4] S. Gemsheim and J. M. Rost: Statistical mechanics from relational complex time with a pure state, Phys. Rev. D 109, L121701 (2024).

The Pareto income distribution arises from a few basic assumptions

Noise, Population Dynamics and Excluded Volume in Active Matter Ronald Dickman1, Tiago Venzel Rosembach1 , 2, Ana Luiza Novaes Dias1, Leonardo Santos Lopes1 1Departamento de F´ısica and National Institute of Science and Technology for Complex Systems, ICEx, Universidade Federal de Minas Gerais, C.P. 702, 30123-970 Belo Horizonte, Minas Gerais, Brazil 22Departamento de Forma¸c˜ao Geral de Leopoldina, Centro Federal de Ensino Tecnol´ogico de Minas Gerais, Rua Jos´e Peres 558, Cento, Leopoldina, Minas Gerais 36700-001, Brazil , I shall review some recent results on Vicseklike models of active matter including population dynamics as well as a minimal lattice model for polar active matter with excluded volume [1]. These studies have also led to insights into the nature of the noise commonly employed in such models. References [1] T. V. Rosembach et al., Phys. Rev E 110, 014109 (2024).

Restoring the fluctuation-dissipation theorem in growth and phase transition through a new emergent fractal dimension Henrique A. Lima (UnB), Edwin E. M. Luis (UFF), Ismael S. S. Carrasco (UnB) Alex Hansen (NTNU), *Fernando A. Oliveira(UnB,UFF) We develop the hypothesis that the dynamics of a given system may lead to a fractal dimension df different from the original spatial dimension d. This phenomenon is more easy to observe near a phase transition. We also speculate how the response function might be sensitive to this change in dimensionality. We discuss how this phenomenon appears in phase transition and growth phenomena. Furthermore, we show that correlations appear as the difference between d − df becomes sensitive, an effect similar to what occurs in growth phenomena[1-6]. Moreover, we determine[7] the Fisher exponent as η = d − df , and the fractal dimension df for the Ising model. We validate it via computer simulations for two dimensions[7]. [1] M. S. Gomes-Filho and F. A. Oliveira, EPL 133 10001 (2021) [2] P. R. H. dos Anjos, W. S. Alves, M. S. Gomes-Filho, D. L. Azevedo and F. A. Oliveira, Frontiers in Physics 9 , 741590 (2021). [3] M. S. Gomes-Filho, A. L. A. Penna and F. A. Oliveira, Results in Physics 26, 104435 (2021). [4] E. E. M. Luis, T. A. de Assis, F. A. Oliveira, Journal of Statistical Mechanics: Theory and Experiment 8, 083202 (2022). [5] E. E. Mozo Luis, F. A. Oliveira, and T. A. de Assis, Phys. Rev. E 107, 034802 (2023). [6] M. S. Gomes-Filho, Pablo de Castro, D. B. Liarte, and F. A. Oliveira, Entropy, 26, 260 (2024). https://www.mdpi.com/1099-4300/26/3/260 [7] H. A. Lima, E. E. M. Luis, I. S. S. Carrasco, A. Hansen, F. A. Oliveira. arXiv preprint arXiv:2402.10167

Entropy of trails on the square lattice in the full lattice limit Lucas R. Rodrigues, Thomas Prellberg, Ju ̈rgen F. Stilck 1 IF-Universidade Federal Fluminense, 2 School of Mathemathical Sciences, Queen Mary University of London, 3 IF-Universidade Federal Fluminense Trails are lattice walks which are constrained to pass through each edge of the lattice at most once [1], they may be seen as a generalization of the self-avoiding walks (SAW’s), which visit each site of the lattice not more than once. On the square lattice, the trail at each site, when the four incident edges are occupied, may have three possible configurations: two collisions, where pairs of perpendicular edges are connected, and a crossing, where pairs of parallel edges connect. We study the model of semi- flexible trails on the square lattice in the compact limit, that is, when the walk passes through all the edges of the lattice and crossings have a statistical weight ω. To obtain estimates for the entropy, we solve the model model numerically on strips of finite widths m using transfer matrices and extrapolate our results to the two-dimensional limit m → ∞. When crossings are forbidden (ω = 0), the model is known as VISAW in the literature and many exact results are known [2]. Another particular limit is ω = 1, where the entropy reaches a maximum, and finally ω → ∞, where no collisions appear and the entropy vanishes. Besides obtaining precise estimates for the entropy as a function of the density of crossings ρx, we also solve the model in a simple mean-field approximation, where loops are allowed, and on the Husimi lattice built with squares [3], comparing the results. References [1] A. R. Massih and M. A. Moore, J. Phys. A 8, 237 (1975), D P Foster, Phys. Rev. E 84 032102 (2011); A Bedini, A L Owczarek and T. Prellberg, Phys. Rev. E 87 012142 (2013). [2] P. W. Kasteleyn, Physica 29, 1329 (1963). [3] T. J. Oliveira and J. F. Stilck, Phys. Rev. E 93 012502 (2017); T. J. Oliveira, W. G. Dantas, T. Prellberg , and J. F. Stilck, J. Phys. A 51 054001 (2018).

Classical Physics and Black Body Radiation The inability of classical physics to account for the experimentally observed fre-quency spectrum of blackbody radiation is at the origin of quantum theory. In spite of desperate attempts, the falloff of the blackbody curve at high frequencies could not be explained by classical mechanics. Here we discuss the properties of the black-body spectrum by direct numerical solution of the classical equations of motion of a one-dimensional model that, however, contains the essential general features of the field-matter interaction. Our approach does not rely on any statistical assumption. We show that the classical blackbody spectrum exhibits remarkable properties: (i) a quasistationary state with low frequency modes thermalized with the matter (ii) consistency with the Stefan-Boltzmann law, and (iii) a high-frequency cutoff. The present work is a preliminary step before addressing ergodicity in quantum field the-ories. This will require a nontrivial extension of concepts and tools recently devel-oped for the investigation of thermalization and localization in many-body quantum systems. Preliminary results on a 3d model are also presented. Reference (*) in collaboration with Jiao Wang and Giuliano Benenti [1] F. R. S. Lord Rayleigh, Philos. Mag. 49 (1900) 539. [2] J. H. Jeans, The Dynamical Theory of Gases, 4th ed., Cambridge University Press, Cambridge, England, 2009. [3] L. Boltzmann, Ann. Phys., Berlin, (1884) 258-291. [4] L. Boltzmann Nature 51 (1895) 413. [5] Jiao Wang, G. Casati and G Benenti, Phys. Rev. Lett. 128 (2022) 134101