arXiv subjects

Rudolf Hanel

Publications and source records attributed to Rudolf Hanel.

At least 19 recordsLinked to original sources

arXiv2026

Metabolic scaling, von Bertalanffy growth and an exponent equation

In this work, we interpret developmental growth as a metabolic energy allocation problem and link the von Bertalanffy growth model to metabolic energy investments into the growth channel. Using a framework that specifies how metabolic energy is allocated among baseline maintenance, growth, and other processes, we analyse the resulting growth allocation patterns and derive direct relationships between key scaling exponents: the mass-growth exponent, the length-based exponent, the metabolic scaling exponent, and the geometric exponent, which describes the mass-length relationship. These exponents determine the metabolic investment exponent, which controls the qualitative behaviour of the growth-allocation function. Requiring the inferred allocation fraction to remain biologically feasible, we derive constraints on developmental velocity and characteristic mass scales. This provides a physical, energy-based interpretation of phenomenological growth curves and clarifies how metabolic scaling, geometric scaling, and growth dynamics are interrelated within a single allocation framework.

q-bio.QM↗

arXiv2026

Gardner volumes and self-organization in a minimal model of complex ecosystems

We study self-organization in a minimally nonlinear model of large random ecosystems. Populations evolve over time according to a piecewise linear system of ordinary differential equations subject to a non-negativity constraint resulting in discrete time extinction and revival events. The dynamics are generated by a random elliptic community matrix with tunable correlation strength. We show that, independent of the correlation strength, solutions of the system are confined to subsets of the phase space that can be cast as time-varying Gardner volumes from the theory of learning in neural networks. These volumes decrease with the diversity (i.e. the fraction of extant species) and become exponentially small in the long-time limit. Using standard results from random matrix theory, the changing diversity is then linked to a sequence of contractions and expansions in the spectrum of the community matrix over time, resulting in a sequence of May-type stability problems determining whether the total population evolves toward complete extinction or unbounded growth. In the case of unbounded growth, we show the model allows for a particularly simple nonlinear extension in which the solutions instead evolve towards a new attractor.

nlin.AO↗

arXiv2025

More Than Opinions: The Role of Values in Shaping Fairness and Status in the Ultimatum Game within Structured Societies

Asymmetric evolutionary games, such as the Ultimatum Game, provide keys to understanding the emergence of fairness in social species. Building on this framework, we explore the evolution of social value systems and the operational role that social status plays in hierarchically organised societies. Within the asymmetric Ultimatum Game paradigm, where "proposers" suggest terms for resource distribution, and "responders" accept or reject these terms, we examine the assignment of roles between players under a subjective social order. This order is grounded in an emergent status hierarchy based on observable player attributes (such as age and wealth). The underlying rules for constructing such a hierarchy stabilise over time by inheritance and family ties. Despite their subjective nature these (often sub-conscious) value systems have operative meaning in controlling access of individuals to resources and decision making. We demonstrate these effects using a simple but sufficiently complex model with dynamical population size and network structure, where division of resources (prey) is carried out according to the principles of the Ultimatum Game. We focus on the emerging proposer and responder thresholds under distinct social hierarchies and interaction networks and discuss them in relation to the extensive body of Ultimatum Game experiments conducted across a wide range of cultural contexts. We observe the emergence of diverse sharing norms, ranging from unfair to highly generous, alongside the development of various social norms.

physics.soc-ph↗

arXiv2025

Thermodynamics of driven systems with explicitly broken detailed balance

In systems with detailed balance, the stationary distribution and the equilibrium distribution are identical, creating a clear connection between energetic and entropic quantities. Many driven systems violate detailed balance and still pose a challenge for a consistent thermodynamic interpretation. Even steady-state potentials like entropy or free energy are no longer state variables. Here, we use a framework for systems with broken detailed balance, where Boltzmann entropy can be computed while properly taking constraints on state transitions into account. As an illustration, we establish the thermodynamic relations for arbitrarily driven sample space-reducing processes that are non-equilibrium but show steady states. We demonstrate that, despite explicitly broken detailed balance, it remains feasible to define and unambiguously interpret the effective thermodynamic potentials.

cond-mat.stat-mech↗

arXiv2024

Typicality, entropy and the generalization of statistical mechanics

When at equilibrium, large-scale systems obey conventional thermodynamics because they belong to microscopic configurations (or states) that are typical. Crucially, the typical states usually represent only a small fraction of the total number of possible states, and yet the characterization of the set of typical states -- the typical set -- alone is sufficient to describe the macroscopic behavior of a given system. Consequently, the concept of typicality, and the associated Asymptotic Equipartition Property allow for a drastic reduction of the degrees of freedom needed for system's statistical description. The mathematical rationale for such a simplification in the description is due to the phenomenon of concentration of measure. The later emerges for equilibrium configurations thanks to very strict constraints on the underlying dynamics, such as weekly interacting and (almost) independent system constituents. The question naturally arises as to whether the concentration of measure and related typicality considerations can be extended and applied to more general complex systems, and if so, what mathematical structure can be expected in the ensuing generalized thermodynamics. In this paper we illustrate the relevance of the concept of typicality in the toy model context of the "thermalized" coin and show how this leads naturally to Shannon entropy. We also show an intriguing connection: The characterization of typical sets in terms of Renyi and Tsallis entropies naturally leads to the free energy and partition function, respectively, and makes their relationship explicit. Finally, we propose potential ways to generalize the concept of typicality to systems where the standard microscopic assumptions do not hold.

cond-mat.stat-mech↗

arXiv2024

Fairness in Multi-Proposer-Multi-Responder Ultimatum Game

The Ultimatum Game is conventionally formulated in the context of two players. Nonetheless, real-life scenarios often entail community interactions among numerous individuals. To address this, we introduce an extended version of the Ultimatum Game, called the Multi-Proposer-Multi-Responder Ultimatum Game. In this model, multiple responders and proposers simultaneously interact in a one-shot game, introducing competition both within proposers and within responders. We derive subgame-perfect Nash equilibria for all scenarios and explore how these non-trivial values might provide insight into proposal and rejection behavior experimentally observed in the context of one vs. one Ultimatum Game scenarios. Additionally, by considering the asymptotic numbers of players, we propose two potential estimates for a "fair" threshold: either 31.8% or 36.8% of the pie (share) for the responder.

math.OC↗

arXiv2022

Homophily-based social group formation in a spin-glass self-assembly framework

Homophily, the tendency of humans to attract each other when sharing similar features, traits, or opinions has been identified as one of the main driving forces behind the formation of structured societies. Here we ask to what extent homophily can explain the formation of social groups, particularly their size distribution. We propose a spin-glass-inspired framework of self-assembly, where opinions are represented as multidimensional spins that dynamically self-assemble into groups; individuals within a group tend to share similar opinions (intra-group homophily), and opinions between individuals belonging to different groups tend to be different (inter-group heterophily). We compute the associated non-trivial phase diagram by solving a self-consistency equation for 'magnetization' (combined average opinion). Below a critical temperature, there exist two stable phases: one ordered with non-zero magnetization and large clusters, the other disordered with zero magnetization and no clusters. The system exhibits a first-order transition to the disordered phase. We analytically derive the group-size distribution that successfully matches empirical group-size distributions from online communities.

cond-mat.stat-mech↗

arXiv2022

Information consumption and size in firms

Social and biological collectives need to exchange information to persist and to function. This happens across internal networks, whose structure represents static channels through which information flows. Less studied is the quantity and variety of information transmitted. We characterize a part of the information flow, the information going into organizations, primarily business firms. We measure what firms read using a data set of hundreds of millions of records of news articles accessed by employees across millions of firms. We measure and relate quantitatively three essential aspects: reading volume, reading variety, and firm size. First we compare volume with firm size, showing that firms grow sublinearly with the volume of their reading. The scaling means that inequality in information volume exaggerates the classic Zipf's law inequality in firm size, pointing to an economy of scale in information consumption. Then, by connecting variety and volume, we show that the firms vary in their reading habits to a limited degree. Firms above a certain size become repetitive readers, consistent with the sudden onset of a coordination cost between teams, not individual employees. Finally, we relate information variety to size to show that large firms tend to increase investments in existing areas of interest instead of divesting from them to move to new areas. We argue that this reflects structural constraints in growth. The results indicate how information consumption reflects the role of internal structure, beyond individual employees, analogous to information processing in other social and biological systems.

physics.soc-ph↗

arXiv2022

Equivalence of information production and generalized entropies in complex processes

Complex systems that are characterized by strong correlations and fat-tailed distribution functions have been argued to be incompatible within the framework of Boltzmann-Gibbs entropy. As an alternative, so-called generalized entropies were proposed and intensively studied. Here we show that this incompatibility is a misconception. For a broad class of processes, Boltzmann entropy the log multiplicity remains the valid entropy concept, however, for non-i.i.d., non-multinomial, and non-ergodic processes, Boltzmann entropy is not of Shannon form. The correct form of Boltzmann entropy can be shown to be identical with generalized entropies. We derive this result for all processes that can be mapped reversibly to adjoint representations where processes are i.i.d.. In these representations the information production is given by the Shannon entropy. We proof that over the original sampling space this yields functionals that are identical to generalized entropies. The problem of constructing adequate context-sensitive entropy functionals therefore can be translated into the much simpler problem of finding adjoint representations. The method provides a comprehensive framework for a statistical physics of strongly correlated systems and complex processes.

cond-mat.stat-mech↗

arXiv2021

The typical set and entropy in stochastic systems with arbitrary phase space growth

The existence of the {\em typical set} is key for data compression strategies and for the emergence of robust statistical observables in macroscopic physical systems. Standard approaches derive its existence from a restricted set of dynamical constraints. However, given the enormous consequences for the understanding of the system's dynamics, and its role underlying the presence of stable, almost deterministic statistical patterns, a question arises whether typical sets exist in much more general scenarios. We demonstrate here that the typical set can be defined and characterized from general forms of entropy for a much wider class of stochastic processes than it was previously thought. This includes processes showing arbitrary path dependence, long range correlations or dynamic sampling spaces; suggesting that typicality is a generic property of stochastic processes, regardless of their complexity. Our results impact directly in the understanding of the stability of complex systems, open the door to new data compression strategies and points to the existence of statistical mechanics-like approaches to systems arbitrarily away from equilibrium with dynamic phase spaces. We argue that the potential emergence of robust properties in complex stochastic systems provided by the existence of typical sets has special relevance to biological systems.

cond-mat.stat-mech↗

arXiv2020

Balanced and fragmented phases in societies with homophily and social balance

Recent attempts to understand the origin of social fragmentation are based on spin models which include terms accounting for two social phenomena: homophily -- the tendency for people with similar opinions to establish positive relations -- and social balance -- the tendency for people to establish balanced triadic relations. Spins represent attribute vectors that encode multiple (binary) opinions of individuals and social interactions between individuals can be positive or negative. Recent work suggests that large systems of N >> 1 individuals never reach a balanced state (where unbalanced triads with one or three hostile links remain), provided the number of attributes for each agent is less than O(N^2) [Phys. Rev. Lett. 125, 078302]. Here we show that this statement is overly restrictive. Within a Hamiltonian framework that minimizes individuals' social stress, we demonstrate that stationary, balanced, but fragmented states can be reached for any number of attributes, if, in addition to homophily, individuals take into account a significant fraction, q, of their triadic relations. Above a critical value q_c, balanced states result. This result also holds for sparse realistic social networks. Finally, in the limit of small q, our result agrees with that of [Phys. Rev. Lett. 125, 078302].

physics.soc-ph↗

arXiv2020

Why are most COVID-19 infection curves linear?

Many countries have passed their first COVID-19 epidemic peak. Traditional epidemiological models describe this as a result of non-pharmaceutical interventions that pushed the growth rate below the recovery rate. In this new phase of the pandemic many countries show an almost linear growth of confirmed cases for extended time-periods. This new containment regime is hard to explain by traditional models where infection numbers either grow explosively until herd immunity is reached, or the epidemic is completely suppressed (zero new cases). Here we offer an explanation of this puzzling observation based on the structure of contact networks. We show that for any given transmission rate there exists a critical number of social contacts, $D_c$, below which linear growth and low infection prevalence must occur. Above $D_c$ traditional epidemiological dynamics takes place, as e.g. in SIR-type models. When calibrating our corresponding model to empirical estimates of the transmission rate and the number of days being contagious, we find $D_c\sim 7.2$. Assuming realistic contact networks with a degree of about 5, and assuming that lockdown measures would reduce that to household-size (about 2.5), we reproduce actual infection curves with a remarkable precision, without fitting or fine-tuning of parameters. In particular we compare the US and Austria, as examples for one country that initially did not impose measures and one that responded with a severe lockdown early on. Our findings question the applicability of standard compartmental models to describe the COVID-19 containment phase. The probability to observe linear growth in these is practically zero.

physics.soc-ph↗

arXiv2020

The effect of social balance on social fragmentation

With the availability of cell phones, internet, social media etc. the interconnectedness of people within most societies has increased drastically over the past three decades. Across the same timespan, we are observing the phenomenon of increasing levels of fragmentation in society into relatively small and isolated groups that have been termed filter bubbles, or echo chambers. These pose a number of threats to open societies, in particular, a radicalisation in political, social or cultural issues, and a limited access to facts. In this paper we show that these two phenomena might be tightly related. We study a simple stochastic co-evolutionary model of a society of interacting people. People are not only able to update their opinions within their social context, but can also update their social links from collaborative to hostile, and vice versa. The latter is implemented such that social balance is realised. We find that there exists a critical level of interconnectedness, above which society fragments into small sub-communities that are positively linked within and hostile towards other groups. We argue that the existence of a critical communication density is a universal phenomenon in all societies that exhibit social balance. The necessity arises from the underlying mathematical structure of a phase transition phenomenon that is known from the theory of a kind of disordered magnets called spin glasses. We discuss the consequences of this phase transition for social fragmentation in society.

physics.soc-ph↗

arXiv2020

Thermodynamics of structure-forming systems

Structure-forming systems are ubiquitous in nature, ranging from atoms building molecules to self-assembly of colloidal amphibolic particles. The understanding of the underlying thermodynamics of such systems remains an important problem. Here we derive the entropy for structure-forming systems that differs from Boltzmann-Gibbs entropy by a term that explicitly captures clustered states. For large systems and low concentrations, the approach is equivalent to the grand-canonical ensemble; for small systems, we find significant deviations. We derive the detailed fluctuation theorem and Crooks' work fluctuation theorem for structure-forming systems. The connection to the theory of particle self-assembly is discussed. We apply the results to several physical systems. We present the phase diagram for patchy particles described by the Kern-Frenkel potential. We show that the Curie-Weiss model with molecule structures exhibits a first-order phase transition.

cond-mat.stat-mech↗

arXiv2020

Boosting test-efficiency by pooled testing strategies for SARS-CoV-2

In the current COVID19 crisis many national healthcare systems are confronted with an acute shortage of tests for confirming SARS-CoV-2 infections. For low overall infection levels in the population, pooling of samples can drastically amplify the testing efficiency. Here we present a formula to estimate the optimal pooling size, the efficiency gain (tested persons per test), and the expected upper bound of missed infections in the pooled testing, all as a function of the populationwide infection levels and the false negative/positive rates of the currently used PCR tests. Assuming an infection level of 0.1 % and a false negative rate of 2 %, the optimal pool size is about 32, the efficiency gain is about 15 tested persons per test. For an infection level of 1 % the optimal pool size is 11, the efficiency gain is 5.1 tested persons per test. For an infection level of 10 % the optimal pool size reduces to about 4, the efficiency gain is about 1.7 tested persons per test. For infection levels of 30 % and higher there is no more benefit from pooling. To see to what extent replicates of the pooled tests improve the estimate of the maximal number of missed infections, we present all results for 1, 3, and 5 replicates.

q-bio.PE↗

arXiv2020

Time-Energy Uncertainty Principle for Irreversible Heat Engines

Even though irreversibility is one of the major hallmarks of any real life process, an actual understanding of irreversible processes remains still mostly semiempirical. In this paper we formulate a thermodynamic uncertainty principle for irreversible heat engines operating with an ideal gas as a working medium. In particular, we show that the time needed to run through such an irreversible cycle multiplied by the irreversible work lost in the cycle, is bounded from below by an irreducible and process-dependent constant that has the dimension of an action. The constant in question depends on a typical scale of the process and becomes comparable to Planck's constant at the length scale of the order Bohr-radius, i.e., the scale that corresponds to the smallest distance on which the ideal gas paradigm realistically applies.

cond-mat.stat-mech↗

arXiv2020

Information geometry of scaling expansions of non-exponentially growing configuration spaces

Many stochastic complex systems are characterized by the fact that their configuration space doesn't grow exponentially as a function of the degrees of freedom. The use of scaling expansions is a natural way to measure the asymptotic growth of the configuration space volume in terms of the scaling exponents of the system. These scaling exponents can, in turn, be used to define universality classes that uniquely determine the statistics of a system. Every system belongs to one of these classes. Here we derive the information geometry of scaling expansions of sample spaces. In particular, we present the deformed logarithms and the metric in a systematic and coherent way. We observe a phase transition for the curvature. The phase transition can be well measured by the characteristic length r, corresponding to a ball with radius 2r having the same curvature as the statistical manifold. Increasing characteristic length with respect to the size of the system is associated with sub-exponential sample space growth is associated with strongly constrained and correlated complex systems. Decreasing of the characteristic length corresponds to super-exponential sample space growth that occurs for example in systems that develop structure as they evolve. Constant curvature means exponential sample space growth that is associated with multinomial statistics, and traditional Boltzmann-Gibbs, or Shannon statistics applies. This allows us to characterize transitions between statistical manifolds corresponding to different families of probability distributions.

cond-mat.stat-mech↗

arXiv2018

The role of grammar in transition-probabilities of subsequent words in English text

Sentence formation is a highly structured, history-dependent, and sample-space reducing (SSR) process. While the first word in a sentence can be chosen from the entire vocabulary, typically, the freedom of choosing subsequent words gets more and more constrained by grammar and context, as the sentence progresses. This sample-space reducing property offers a natural explanation of Zipf's law in word frequencies, however, it fails to capture the structure of the word-to-word transition probability matrices of English text. Here we adopt the view that grammatical constraints (such as subject--predicate--object) locally re-order the word order in sentences that are sampled with a SSR word generation process. We demonstrate that superimposing grammatical structure -- as a local word re-ordering (permutation) process -- on a sample-space reducing process is sufficient to explain both, word frequencies and word-to-word transition probabilities. We compare the quality of the grammatically ordered SSR model in reproducing several test statistics of real texts with other text generation models, such as the Bernoulli model, the Simon model, and the Monkey typewriting model.

cs.CL↗