arXiv subjects

Henrik Jeldtoft Jensen

Publications and source records attributed to Henrik Jeldtoft Jensen.

At least 19 recordsLinked to original sources

arXiv2026

Fisher Information Metric as a model-free measure of proximity to criticality in neural systems

Critical phenomena are widespread across many disciplines and have recently become a topic of deep interest in the study of biological and artificial neural networks. A distinct signature of criticality is the emergence of avalanches with power-law-distributed sizes and durations. However, empirically estimating the critical exponents remains challenging, and their interpretation is often model-dependent. In this work, we demonstrate how the Fisher Information Metric (FIM), a measure of generalized susceptibility, provides a comprehensive, model-agnostic characterization of the critical region in neural systems. We validate this approach across models of increasing biological complexity, from prototypical branching processes to spiking and whole-brain models, showing that FIM of each model's control parameter reliably tracks the system's degree of criticality. To emulate the study of real-world systems, where the control parameter is unknown, we additionally calculate FIM of the observed branching ratio of neural activity. The resulting FIM peaks where activity growth and decay balance, with the peak sharpening as the system approaches criticality. Hence, FIM peak width and height yield continuous, model-free readouts of proximity to criticality without requiring knowledge of the true control parameter, offering a robust tool for probing criticality in neural systems.

q-bio.NC↗

arXiv2026

Universality classes, Thermodynamics of Group Entropies, and Black Holes

Conventional Boltzmann--Gibbs statistical mechanics successfully describes systems with weak to moderate correlations, where the number of accessible configurations $W(N)$ grows exponentially with the number of degrees of freedom~$N$. However, this framework breaks down for systems with strong correlations or long-range interactions, for which the configuration space exhibits non-exponential growth. While numerous generalized entropies have been proposed to address this limitation, a coherent link to classical thermodynamic laws has remained elusive. Here, we propose group entropies as a unifying framework, defining universality classes of entropies through the asymptotic scaling of $W(N)$, each yielding an extensive entropy. We show that this approach provides the basis for a consistent thermodynamic formulation beyond the Boltzmann--Gibbs paradigm. In particular, by expressing these entropies in terms of thermodynamic state variables and taking the thermodynamic limit, we demonstrate their consistency with classical thermodynamics, in close analogy to the emergence of the Clausius entropy from the Boltzmann--Gibbs formalism. Focusing on the zeroth thermodynamic law, we identify the empirical temperature and, by using Carathéodory's formulation of the second law, we derive the associated absolute temperature. As an application of the thermodynamic framework obtained, we analyze black-hole thermodynamics using the group entropy class corresponding to stretched-exponential behavior of $W(N)$. In particular, we show that a hallmark property of black holes -- their negative specific heat -- emerges naturally within this framework while the entropy remains extensive. This result holds for the stretched-exponential entropies associated with both the Bekenstein--Hawking and Barrow entropy scalings.

cond-mat.stat-mech↗

arXiv2025

Directionality measures in evolutionary ecological networks: Insights from the Tangled Nature model

The myriad microscopic interactions among the individual organisms that constitute an ecological system collectively give rise, at the macroscopic scale, to evolutionary trends. The ability to detect the directionality of such trends is crucial for understanding and managing the dynamics of natural systems. Nevertheless, identifying the key observable quantities that capture such directional behaviour poses a major challenge. In this study, we propose that translating ecological data into a network framework is a valuable strategy to measure system stability and evolution. We examine the Tangled Nature model as a test case, evaluating network entropy, species diversity, and the clustering coefficient as metrics of network stability and directionality.

q-bio.PE↗

arXiv2025

Group structure as a foundation for entropies

Entropy can signify different things: For instance, heat transfer in thermodynamics or a measure of information in data analysis. Many entropies have been introduced and it can be difficult to ascertain their different importance and merits. Here we consider entropy in an abstract sense, as a functional on a probability space and we review how being able to handle the trivial case of non-interacting systems together with the subtle requirement of extensivity allows a systematic classification of the functional form.

math-ph↗

arXiv2025

Simple physical systems as a reference for multivariate information dynamics

Understanding a complex system entails capturing the non-trivial collective phenomena that arise from interactions between its different parts. Information theory is a flexible and robust framework to study such behaviours, with several measures designed to quantify and characterise the interdependencies among the system's components. However, since these estimators rely on the statistical distributions of observed quantities, it is crucial to examine the relationships between information-theoretic measures and the system's underlying mechanistic structure. To this end, here we present an information-theoretic analytical investigation of an elementary system of interactive random walkers subject to Gaussian noise. Focusing on partial information decomposition, causal emergence, and integrated information, our results help us develop some intuitions on their relationship with the physical parameters of the system. For instance, we observe that uncoupled systems can exhibit emergent properties, in a way that we suggest may be better described as ''statistically autonomous''. Overall, we observe that in this simple scenario information measures align more reliably with the system's mechanistic properties when calculated at the level of microscopic components, rather than their coarse-grained counterparts, and over timescales comparable with the system's intrinsic dynamics. Moreover, we show that approaches that separate the contributions of the system's dynamics and steady-state distribution (e.g. via causal perturbations) may help strengthen the interpretation of information-theoretic analyses.

cs.IT↗

arXiv2024

Extensive Composable Entropy for the Analysis of Cosmological Data

Along recent decades, an intensive worldwide research activity is focusing both black holes and cosmos (e.g. the dark-energy phenomenon) on the basis of entropic approaches. The Boltzmann-Gibbs-based Bekenstein-Hawking entropy $S_{BH}\propto A/l_P^2$ ($A \equiv$ area; $l_P \equiv$ Planck length) systematically plays a crucial theoretical role although it has a serious drawback, namely that it violates the thermodynamic extensivity of spatially-three-dimensional systems. Still, its intriguing area dependence points out the relevance of considering the form $W(N)\sim μ^{N^γ}\;\;(μ>1;γ>0)$, $W$ and $N$ respectively being the total number of microscopic possibilities and the number of components; $γ=1$ corresponds to standard Boltzmann-Gibbs (BG) statistical mechanics. For this $W(N)$ asymptotic behavior, we introduce here, on a group-theory basis, the entropic functional $S_{α,γ}=k \Bigl[ \frac{\ln Σ_{i=1}^W p_i^α}{1-α} \Bigr]^{\frac{1}γ} \;(α\in \mathbb{R};\,S_{1,1}=S_{BG}\equiv-k\sum_{i=1}^W p_i \ln p_i)$. This functional simultaneously is {\it extensive} (as required by thermodynamics) and {\it composable} (as required for logic consistency), $\forall (α,γ)$. We further show that $(α,γ)=(1,2/3)$ satisfactorily agrees with cosmological data measuring neutrinos, Big Bang nucleosynthesis and the relic abundance of cold dark matter particles, as well as dynamical and geometrical cosmological data sets.

cond-mat.stat-mech↗

arXiv2022

Emergence of universal scaling in weather extreme events

The frequency and magnitude of weather extreme events have increased significantly during the past few years in response to anthropogenic climate change. However, global statistical characteristics and underlying physical mechanisms are still not fully understood. Here, we adopt a statistical physics and probability theory based method to investigate the nature of extreme weather events, particularly the statistics of the day-to-day air temperature differences. These statistical measurements reveal that the distributions of the magnitudes of the extreme events satisfy a universal \textit{Gumbel} distribution, while the waiting time of those extreme events is governed by a universal \textit{Gamma} function. Further finite-size effects analysis indicates robust scaling behaviours. We additionally unveil that the cumulative distribution of logarithmic waiting times between the record events follows an \textit{Exponential} distribution and that the evolution of this climate system is directional where the underlying dynamics are related to a decelerating release of tension. The universal scaling laws are remarkably stable and unaffected by global warming. Counterintuitively, unlike as expected for record dynamics, we find that the number of quakes of the extreme temperature variability does not decay as one over time but with deviations relevant to large-scale climate extreme events. Our theoretical framework provides a fresh perspective on the linkage of universality, scaling, and climate systems. The findings throw light on the nature of the weather variabilities and could guide us to better forecast extreme events.

physics.ao-ph↗

arXiv2022

Spontaneous Emergence of Computation in Network Cascades

Neuronal network computation and computation by avalanche supporting networks are of interest to the fields of physics, computer science (computation theory as well as statistical or machine learning) and neuroscience. Here we show that computation of complex Boolean functions arises spontaneously in threshold networks as a function of connectivity and antagonism (inhibition), computed by logic automata (motifs) in the form of computational cascades. We explain the emergent inverse relationship between the computational complexity of the motifs and their rank-ordering by function probabilities due to motifs, and its relationship to symmetry in function space. We also show that the optimal fraction of inhibition observed here supports results in computational neuroscience, relating to optimal information processing.

physics.soc-ph↗

arXiv2021

New probability distribution describing emergence in state space

We revisit the pairing model of state spaces with new emergent states introduced in J. Phys. A: Math. Theor. 51 375002, 2018. We facilitate our analysis by introducing a simplified pairing model consisting of balls able to form pairs but without any internal structure. For both the simplified and the original model we compute exactly the probability distribution for observing a state with $n_p$ pairs. We show this distribution satisfies a large deviation principle with speed $n \ln(n)$. We present closed form expressions for a variety of statistical quantities including moments and marginal distributions.

cond-mat.stat-mech↗

arXiv2021

Brain, Rain and Forest Fires -- What is critical about criticality: In praise of the correlation function

We present a brief review of power laws and correlation functions as measures of criticality and the relation between them. By comparing phenomenology from rain, brain and the forest fire model we discuss the relevant features of self-organisation to the vicinity about a critical state. We conclude that organisation to a region of extended correlations and approximate power laws may be behaviour of interest shared between the three considered systems.

cond-mat.stat-mech↗

arXiv2020

Record dynamics of evolving metastable systems: theory and applications

Record Dynamics (RD) deals with complex systems evolving through a sequence of metastable stages. These are macroscopically distinguishable and appear stationary, except for the sudden and rapid changes, called quakes, which induce the transitions from one stage to the next. This phenomenology is well known in physics as "physical aging", but from the vantage point of RD the evolution of a class of systems of physical, biological and cultural origin is rooted in a hierarchically structured configuration space and can therefore be analyzed by similar statistical tools. This colloquium paper strives to present in a coherent fashion methods and ideas that have gradually evolved over time. To this end, it first describes the differences and similarities between RD and two widespread paradigms of complex dynamics, Self Organized Criticality and Continuous Time Random Walks. It then outlines the Poissonian nature of records events in white noise time series, and connects it to the statistics of quakes in metastable hierarchical systems, arguing that the relaxation effects of quakes can generally be described by power laws unrelated to criticality. Several different applications of RD have been developed over the years. Some of these are described, showinghe basic RD hypothesis, the log time homogeneity of quake dynamics, can be empirically verified in a given context. The discussion summarizes the paper and briefly mentions applications not discussed in detail. Finally, the outlook points to possible improvements and to new areas of research where RG could be of use.

cond-mat.stat-mech↗

arXiv2020

Distribution of neighborhood size in cities

We study the distribution of neighborhoods across a set of 12 global cities and find that the distribution of neighborhood sizes follows exponential decay across all cities under consideration. We are able to analytically show that this exponential distribution of neighbourhood sizes is consistent with the observed Zipf's Law for city sizes. We attempt to explain the emergence of exponential decay in neighbourhood size using a model of neighborhood dynamics where migration into and movement within the city are mediated by wealth. We find that, as observed empirically, the model generates exponential decay in neighborhood size distributions for a range of parameter specifications. The use of a comparative wealth-based metric to assess the relative attractiveness of a neighborhood combined with a stringent affordability threshold in mediating movement within the city are found to be necessary conditions for the the emergence of the exponential distribution. While an analytical treatment is difficult due to the globally coupled dynamics, we use a simple two-neighbourhood system to illustrate the precise dynamics yielding equilibrium non-equal neighborhood size distributions.

physics.soc-ph↗

arXiv2020

Spread of Covid-19 in urban neighbourhoods and slums of the developing world

We study the spread of Covid-19 across neighbourhoods of cities in the developing world and find that small numbers of neighbourhoods account for a majority of cases (k-index~0.7). We also find that the countrywide distribution of cases across states/provinces in these nations also displays similar inequality, indicating self-similarity across scales. Neighbourhoods with slums are found to contain the highest density of cases across all cities under consideration, revealing that slums constitute the most at-risk urban locations in this epidemic. We present a stochastic network model to study the spread of a respiratory epidemic through physically proximate and accidental daily human contacts in a city, and simulate outcomes for a city with two kinds of neighbourhoods - slum and non-slum. The model reproduces observed empirical outcomes for a broad set of parameter values - reflecting the potential validity of these findings for epidemic spread in general, especially across cities of the developing world. We also find that distribution of cases becomes less unequal as the epidemic runs its course, and that both peak and cumulative caseloads are worse for slum neighbourhoods than non-slums at the end of an epidemic. Large slums in the developing world therefore contain the most vulnerable populations in an outbreak, and the continuing growth of metropolises in Asia and Africa presents significant challenges for future respiratory outbreaks from perspectives of public health and socioeconomic equity.

physics.soc-ph↗

arXiv2020

Poverty in the time of epidemic: A modelling perspective

We create a network model to study the spread of an epidemic through physically proximate and accidental daily human contacts in a city, and simulate outcomes for two kinds of agents - poor and non-poor. Under non-intervention, peak caseload is maximised, but no differences are observed in infection rates across poor and non-poor. Introducing interventions to control spread, peak caseloads are reduced, but both cumulative infection rates and current infection rates are systematically higher for the poor than for non-poor, across all scenarios. Larger populations, higher fractions of poor, and longer durations of intervention are found to progressively worsen outcomes for the poor; and these are of particular concern for economically vulnerable populations in cities of the developing world. Addressing these challenges requires a deeper, more rigorous understanding of the relationships between structural poverty and epidemy, as well as effective utilization of extant community level infrastructure for primary care in developing cities. Finally, improving iniquitous outcomes for the poor creates better outcomes for the whole population, including the non-poor.

physics.soc-ph↗

arXiv2020

Dynamics of reallocation within India's income distribution

We investigate the nature and extent of reallocation occurring within the Indian income distribution, with a particular focus on the dynamics of the bottom of the distribution. Specifically, we use a stochastic model of Geometric Brownian Motion with a reallocation parameter that was constructed to capture the quantum and direction of composite redistribution implied in the income distribution. It is well known that inequality has been rising in India in the recent past, but the assumption has been that while the rich benefit more than proportionally from economic growth, the poor are also better off than before. Findings from our model refute this, as we find that since the early 2000s reallocation has consistently been negative, and that the Indian income distribution has entered a regime of perverse redistribution of resources from the poor to the rich. Outcomes from the model indicate not only that income shares of the bottom decile (~1%) and bottom percentile (~0.03%) are at historic lows, but also that real incomes of the bottom decile (-2.5%) and percentile (-6%) have declined in the 2000s. We validate these findings using income distribution data and find support for our contention of persistent negative reallocation in the 2000s. We characterize these findings in the context of increasing informalization of the workforce in the formal manufacturing and service sectors, as well as the growing economic insecurity of the agricultural workforce in India. Significant structural changes will be required to address this phenomenon.

econ.EM↗

arXiv2020

The Forest Fire Model: The subtleties of criticality and scale invariance

Amongst the numerous models introduced with SOC, the Forest Fire Model (FFM) is particularly attractive for its close relationship to stochastic spreading, which is central to the study of systems as diverse as epidemics, rumours, or indeed, fires. However, since its introduction, the nature of the model's scale invariance has been controversial, and the lack of scaling observed in many studies diminished its theoretical attractiveness. In this study, we analyse the behaviour of the tree density, the average cluster size and the largest cluster and show that the model could be of high practical relevance for the activation dynamics seen in brain and rain studies. From this perspective, its peculiar scaling properties should be regarded as an asset rather than a limitation.

cond-mat.stat-mech↗

arXiv2020

Economic complexity and capabilities of Indian States

We explore economic competitiveness of Indian states based on the economic complexity algorithm, using a pair of coupled non-linear maps to characterize the Fitness of states and Complexity of products exported by them. We find that states produce almost all products within their productive capabilities - diversifying rather than specializing, and that the probability of coexistence of any pair of productive capabilities is maximized when capabilities are of similar complexity. Therefore, states require long time horizons to build complex capabilities and diverse products. We contextualize Fitness using human development, and find an emergent typology of states. Of most concern are the states of Odisha, Uttar Pradesh, and Bihar, stuck in vicious feedback cycles of poor economic complexity and low human development. Economic complexity also reveals significant concerns with the economic trajectories of Punjab, Gujarat, and West Bengal. We discuss these emergent trends within the framework of India's modern economic history.

physics.soc-ph↗

arXiv2019

Universality Classes and Information-Theoretic Measures of Complexity via Group Entropies

We introduce a class of information measures based on group entropies, allowing us to describe the information-theoretical properties of complex systems. These entropic measures are nonadditive, and are mathematically deduced from a series of natural requirements. In particular, we introduce an extensivity postulate as a natural requirement for an information measure to be meaningful. The information measures proposed are suitably defined for describing universality classes of complex systems, each characterized by a specific phase space growth rate function.

cond-mat.stat-mech↗