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Erik Aurell

Publications and source records attributed to Erik Aurell.

At least 19 recordsLinked to original sources
arXiv2026

The real butterfly effect: from the pop culture to mathematics and physics

The "butterfly effect", introduced over half a century ago by Edward Lorenz, has shifted from a cornerstone of dynamical systems to a popular metaphor, yet its true physical manifestation in fully developed turbulence spans a spectrum of phenomena from standard chaotic sensitivity to the recently established concept of Eulerian spontaneous stochasticity. This paper presents an attempt at a systematic synthesis that brings these different but interconnected ideas together within the unifying framework of the Finite Size Lyapunov Exponent (FSLE). The FSLE describes the growth rate of perturbations as a function of their scale, enabling a comprehensive characterization of the multiscale physics of turbulent flows. Using the FSLE and the Sabra shell model, extended to include thermal noise, we bridge the classical, small-scale Lyapunov regime with predictability at large scales and its interpretation in terms of Eulerian spontaneous stochasticity. Moreover, using the FSLE and the Kraichnan model, we also illustrate the closely related phenomenon of Lagrangian spontaneous stochasticity. To complete the spectrum of butterfly effects, we also examine the "literal butterfly" scenario of localized, sub-dissipative perturbations. Ultimately, this synthesis clarifies the physical mechanisms that dictate the fundamental boundaries of forecasting in high-Reynolds-number flows.

nlin.CD↗
arXiv2026

High-temperature limit penalizing high-frequency quantum fluctuations

We revisit the Caldeira-Leggett model of quantum Brownian motion with Ohmic spectral density, and derive an additional contribution to the decoherence kernel in a new high-temperature limit at arbitrarily large cut-off frequency. This contribution reveals a novel mechanism for the classicalization of high-frequency quantum fluctuations. We further demonstrate that it leads to a Markovian master equation that is in guaranteed Lindblad form, and argue that this master equation describes the correct Markovian limit of quantum Brownian motion. Our approach considers in detail the behavior of the decoherence kernel at both the initial and final times of the process on the time scale of the bath memory.

quant-ph↗
arXiv2026

Fitness Inference in Presence of Migrations between Coupled Evolving Populations

The phase of Quasi-Linkage Equilibrium (QLE) in evolutionary populations is analogous to the thermal equilibrium state in statistical mechanics, a concept pioneered by Kimura in 1965 for two-locus two-allele models. QLE describes a stationary state maintained by the interplay of selection, mutation, recombination and genetic drift. Here we extend QLE theory to populations connected by migration, a fundamental evolutionary force that couples the evolutionary dynamics of interacting subpopulations. Specifically, we examine two populations interacting via symmetric or asymmetric migration while evolving under multi-locus selection. Using whole-genome time-series data generated through FFPopSim, we demonstrate that the QLE phase persists under conditions of sufficiently low migration rates. In this regime, we derive analytical inference relations that allow for the accurate and quantitative estimation of both additive fitness and epistatic interactions.

q-bio.PE↗
arXiv2026

Classification of SARS-CoV-2 Variants through The Epistatical Circos Plots with Convolutional Neural Networks

The COVID-19 pandemic has profoundly affected global health, driven by the remarkable transmissibility and mutational adaptability of the SARS-CoV-2 virus. Although five variants of concern, Alpha, Beta, Gamma, Delta, and Omicron, have been identified, the classification task in this study is formulated using four classes: Alpha, Delta, Omicron, and Else, reflecting the sequence availability and temporal coverage of the dataset. Here, we develop an integrative framework that combines direct coupling analysis (DCA), Circos-based visualization, and convolutional neural networks (CNNs) to characterize lineage-specific epistatic signatures from large-scale SARS-CoV-2 genomic sequences. DCA-inferred pairwise mutational couplings were transformed into Circos images, which were then used as inputs for CNN-based classification models. The proposed framework achieved robust variant classification, with the best-performing model reaching a weighted-average F1-score of $98.68\pm 0.75\%$ and an AUC close to 1.

q-bio.GN↗
arXiv2025

Fitness inference tested by in silico population genetics

We consider populations evolving according to natural selection, mutation, and recombination, and assume that the genomes of all or a representative selection of individuals are known. We pose the problem if it is possible to infer fitness parameters and genotype fitness order from such data. We tested this hypothesis in simulated populations. We delineate parameter ranges where this is possible and other ranges where it is not.Our work provides a framework for determining when fitness inference is feasible from population-wide, whole-genome, time-stratified data and highlights settings where it is not. We give a brief survey of biological model organisms and human pathogens that fit into this framework.

q-bio.PE↗
arXiv2025

Average entanglement entropy of a small subsystem in a constrained pure Gaussian state ensemble

We consider ensembles of pure Gaussian states parametrized by single-mode marginals and (optionally) specific mode-mode correlations. Such ensembles provide a model for the final states when isolated quantum systems thermalize, as they can reproduce thermal properties locally, while being globally pure. By an analysis using real replicas and the coherent state representation of Gaussian states we show that the average entanglement entropy of a small subsystem is the same as the von Neumann entropy of a mixed Gaussian state with the same marginals, but no correlations. Finally, we discuss how these ensembles provide a model for Hawking radiation assuming unitary evolution, and discuss some of their properties in relations to the Page curve of Hawking radiation.

quant-ph↗
arXiv2025

Random pure Gaussian states and Hawking radiation

A black hole evaporates by Hawking radiation. Each mode of that radiation is thermal. If the total state is nevertheless to be pure, modes must be entangled. Estimating the minimum size of this entanglement has been an important outstanding issue. We develop a new theory of constrained random symplectic transformations, based on that the total state is pure and Gaussian with given marginals. In the random constrained symplectic model we then compute the distribution of mode-mode correlations, from which we bound mode-mode entanglement. Modes of frequency much larger than $\frac{k_B T_{H}(t)}{\hbar}$ are not populated at time $t$ and drop out of the analysis. Among the other modes we find that correlations and hence entanglement between relatively thinly populated modes (early-time high-frequency modes and/or late modes of any frequency) to be strongly suppressed. Relatively highly populated modes (early-time low-frequency modes) can on the other hand be strongly correlated, but a detailed analysis reveals that they are nevertheless very unlikely to be entangled. Our analysis hence establishes that restoring unitarity after a complete evaporation of a black hole does not require any significant quantum entanglement between any pair of Hawking modes. Our analysis further gives exact general expressions for the distribution of mode-mode correlations in random, pure, Gaussian states with given marginals, which may have applications beyond black hole physics.

gr-qc↗
arXiv2024

Two fitness inference schemes compared using allele frequencies from 1,068,391 sequences sampled in the UK during the COVID-19 pandemic

Throughout the course of the SARS-CoV-2 pandemic, genetic variation has contributed to the spread and persistence of the virus. For example, various mutations have allowed SARS-CoV-2 to escape antibody neutralization or to bind more strongly to the receptors that it uses to enter human cells. Here, we compared two methods that estimate the fitness effects of viral mutations using the abundant sequence data gathered over the course of the pandemic. Both approaches are grounded in population genetics theory but with different assumptions. One approach, tQLE, features an epistatic fitness landscape and assumes that alleles are nearly in linkage equilibrium. Another approach, MPL, assumes a simple, additive fitness landscape, but allows for any level of correlation between alleles. We characterized differences in the distributions of fitness values inferred by each approach and in the ranks of fitness values that they assign to sequences across time. We find that in a large fraction of weeks the two methods are in good agreement as to their top-ranked sequences, i.e., as to which sequences observed that week are most fit. We also find that agreement between ranking of sequences varies with genetic unimodality in the population in a given week.

q-bio.PE↗
arXiv2023

A perspective on Lindblad's Non-Equilibrium Entropy

Göran Lindblad in 1983 published a monograph on non-equilibrium thermodynamics. We here summarize the contents of this book, and provide a perspective on its relation to later developments in statistical physics and quantum physics. We high-light two aspects. The first is the idea that while all unitaries can be allowed in principle, different theories result from limiting which unitary evolutions are realized in the real world. The second is that Lindblad's proposal for thermodynamic entropy (as opposed to information-theoretic entropy) foreshadows much more recent investigations into optimal quantum transport which is a current research focus in several fields.

quant-ph↗
arXiv2023

Statistical Genetics in and out of Quasi-Linkage Equilibrium (Extended)

This review is about statistical genetics, an interdisciplinary topic between statistical physics and population biology. The focus is on the phase of quasi-linkage equilibrium (QLE). Our goals here are to clarify under which conditions the QLE phase can be expected to hold in population biology and how the stability of the QLE phase is lost. The QLE state, which has many similarities to a thermal equilibrium state in statistical mechanics, was discovered by M Kimura for a two-locus two-allele model, and was extended and generalized to the global genome scale by (Neher and Shraiman, 2011). What we will refer to as the Kimura-Neher-Shraiman (KNS) theory describes a population evolving due to the mutations, recombination, natural selection and possibly genetic drift. A QLE phase exists at sufficiently high recombination rate and/or mutation rates with respect to selection strength. We show how in QLE it is possible to infer the epistatic parameters of the fitness function from the knowledge of the (dynamical) distribution of genotypes in a population. We further consider the breakdown of the QLE regime for high enough selection strength. We review recent results for the selection-mutation and selection-recombination dynamics. Finally, we identify and characterize a new phase which we call the non-random coexistence (NRC) where variability persists in the population without either fixating or disappearing.

q-bio.PE↗
arXiv2022

A closure for the Master Equation starting from the Dynamic Cavity Method

We consider classical spin systems evolving in continuous time with interactions given by a locally tree-like graph. Several approximate analysis methods have earlier been reported based on the idea of Belief Propagation / cavity method. We introduce a new such method which can be derived in a more systematic manner, and which performs better on several important classes of problems.

cond-mat.stat-mech↗
arXiv2022

The double doors of the horizon

In statistical mechanics entropy is a measure of disorder obeying Boltzmann's formula $S=\log{\cal N}$, where ${\cal N}$ is the accessible phase space volume. In black hole thermodynamics one associates to a black hole an entropy Bekenstein-Hawking $S_{BH}$. It is well known that $S_{BH}$ is very large for astrophysical black holes, much larger than any collection of material objects that could have given rise to the black hole. If $S_{BH}$ is an entropy the question is thus what is the corresponding ${\cal N}$, and how come this very large phase space volume is only opened up to the universe by a gravitational collapse, which from another perspective looks like a massive loss of possibilities. I advance a hypothesis that the very large increase in entropy can perhaps be understood as an effect of classical gravity, which eventually bottoms out when quantum gravity comes into play. I compare and discuss a selection of the very rich literature around these questions.

gr-qc↗
arXiv2022

Temporal epistasis inference from more than 3,500,000 SARS-CoV-2 Genomic Sequences

We use Direct Coupling Analysis (DCA) to determine epistatic interactions between loci of variability of the SARS-CoV-2 virus, segmenting genomes by month of sampling. We use full-length, high-quality genomes from the GISAID repository up to October 2021, in total over 3,500,000 genomes. We find that DCA terms are more stable over time than correlations, but nevertheless change over time as mutations disappear from the global population or reach fixation. Correlations are enriched for phylogenetic effects, and in particularly statistical dependencies at short genomic distances, while DCA brings out links at longer genomic distance. We discuss the validity of a DCA analysis under these conditions in terms of a transient Quasi-Linkage Equilibrium state. We identify putative epistatic interaction mutations involving loci in Spike.

q-bio.GN↗
arXiv2022

The mighty force: statistical inference and high-dimensional statistics

This is a review to appear as a contribution to the edited volume "Spin Glass Theory & Far Beyond - Replica Symmetry Breaking after 40 Years", World Scientific. It showcases a selection of contributions from the spin glass community at large to high-dimensional statistics, by focusing on three important graph-based models and methodologies having deeply impacted the field: inference of graphs (a.k.a. direct coupling analysis), inference from graphs (the community detection problem), and the dynamic cavity method, which in particular allows for inference from graphs encoding causal relations.

cond-mat.dis-nn↗
arXiv2022

Quantum information in Hawking radiation

In 1974 Steven Hawking showed that black holes emit thermal radiation, which eventually causes them to evaporate. The problem of the fate of information in this process is known as the "black hole information paradox". Two main types of resolution postulate either a fundamental loss of information in Nature -- hence the breakdown of quantum mechanics -- or some sort of new physics, e.g. quantum gravity, which guarantee the global preservation of unitarity. Here we explore the second possibility with the help of recent developments in continuous-variable quantum information. Concretely, we employ the solution to the Gaussian quantum marginal problem to show that the thermality of all individual Hawking modes is consistent with a global pure state of the radiation. Surprisingly, we find out that the mods of radiation of an astrophysical black hole are thermal until the very last burst. In contrast, the single-mode thermality of Hawking radiation originating from microscopic black holes, expected to evaporate through several quanta, is not excluded, though there are constraints on modes' frequencies. Our result paves the way towards a systematic study of multi-mode correlations in Hawking radiation.

gr-qc↗
arXiv2021

Mutation frequency time series reveal complex mixtures of clones in the world-wide SARS-CoV-2 viral population

We compute the allele frequencies of the alpha (B.1.1.7), beta (B.1.351) and delta (B.167.2) variants of SARS-CoV-2 from almost two million genome sequences on the GISAID repository. We find that the frequencies of a majority of the defining mutations in alpha rose towards the end of 2020 but drifted apart during spring 2021, a similar pattern being followed by delta during summer of 2021. For beta we find a more complex scenario with frequencies of some mutations rising and some remaining close to zero. Our results point to that what is generally reported as single variants is in fact a collection of variants with different genetic characteristics. For all three variants we further find some alleles with a clearly deviating time series.

q-bio.PE↗
arXiv2021

The quantum network as an environment

quantum system interacting with other quantum systems experiences these other systems asan effective environment. The environment is the result of integrating out all the other degrees of freedom in the network, and can be represented by a Feynman-Vernon influence functional (IF)acting on system of interest. A network is characterized by the constitutive systems, how they interact, and the topology of those interactions. Here we show that for networks having the topology of locally tree-like graphs, the Feynman-Vernon influence functional can be determined in a new version of the cavity or Belief Propagation (BP) method. In the BP update stage, cavity IFs are mapped to cavity IFs, while in the BP output stage cavity IFs are combined to output IFs. We compute the fixed point of of this version of BP for harmonic oscillator systems interacting uniformly. We discuss Replica Symmetry and the effects of disorder in this context.

quant-ph↗