arXiv subjects

Christopher P. Kempes

Publications and source records attributed to Christopher P. Kempes.

At least 19 recordsLinked to original sources

arXiv2026

Elemental Stoichiometry as an Ecological Biosignature with Applications to Life Detection

The vast chemical space of possible small molecules, estimated at 10^60 compounds for molecules composed of just C, N, O, and S, is only sparsely occupied by biology. We propose that where life selects molecules within this space constitutes a detectable ecological signature: a fingerprint not of specific compounds, but of the statistical structure of elemental composition across molecules sam-pled from ecological systems. Here we introduce a framework combining Van Krevelen diagrams and element scaling laws to characterize the elemental composition of regions of chemical space occupied by biological systems and contrast them with other chemical systems. Applying this framework to 11,834 microbial metagenomic samples, we show that microbial metabolisms occupy a region of chemical space, which is enriched in heteroatoms such as P, S, N, and O relative to C, shifted toward higher O:C and H:C ratios. We observe sublinear element scaling with system size, yielding insights into how elemental constraints dictate how biological systems occupy chemical space. These patterns are distinct from a sample of 18,000 compounds from the comprehensive Reaxys synthetic chemical database. Critically, datasets from molecules detected in planetary science mission data occupy statistically distinct regions from both terrestrial biological and Reaxys distributions, demonstrating that with standardized methods for data collection, the approach could be developed to discriminate biotic from abiotic chemical signatures in small molecule data from planetary science missions. Our work shows how a combination of Van Krevelen fingerprinting and elemental scaling laws can provide a new class of ecological biosignatures for life detection leveraging mass spectrometric data from planetary missions, which could generalize beyond Earth's specific biochemistry.

q-bio.BM↗

arXiv2026

Computational foundations of the human world

Human societies continuously transform scattered information into collective judgments and coordinated action, whether through markets discovering prices, governments allocating resources, communities enforcing norms, or science converging on reliable claims. Importantly, the computational difficulty of collective decision-making, particularly the time and communication required to reach solutions, imposes fundamental constraints on social organization. While theoretical computer science offers formal tools for analyzing such problems, for instance, by analyzing resource requirements, including time and memory, surprisingly, there is no domain of social science that focuses on the nature of computation in the human world. This perspective argues that we now have the opportunity to deploy these computational frameworks to study human social organization, opening research directions at the intersection of computer science and social science. We highlight core social phenomena that can be framed as computational, including (i) distributed consensus and coordinated action, (ii) societal restructuring with scale, (iii) hierarchical and modular structure, and (iv) externalized memory systems. We identify several concepts from theoretical computer science that may provide insight into these phenomena, especially emphasizing more recently developed approaches beyond the paradigm of Turing~Machines and worst-case computational complexity.

cs.SI↗

arXiv2026

Toward a general theory for the universality and scaling in critical thermal responses in biology

We developed a theory showing that under appropriate normalizations and rescalings, temperature response curves show a remarkably regular behavior and follow a general, universal law. The impressive universality of temperature response curves remained hidden due to various curve-fitting models not well-grounded in first principles. In addition, this framework has the potential to explain the origin of different scaling relationships in thermal performance in biology, from molecules to ecosystems. Here, we summarize the background, principles and assumptions, predictions, implications, and possible extensions of this theory.

q-bio.OT↗

arXiv2026

Predicting Company Growth using Scaling Theory informed Machine Learning

Predicting company growth is a critical yet challenging task because observed dynamics blend an underlying structural growth trend with volatile fluctuations. Here, we propose a Scaling-Theory-Informed Machine Learning (STIML) framework that integrates a scaling-based growth model to capture the mechanism-driven average trend, together with a data-driven forecasting model to learn the residual fluctuations. Using Compustat annual financial statement data (1950--2019) for 31,553 North American companies, we extend the growth model beyond assets to multiple financial indicators, and evaluate STIML against growth model-only and purely data-driven baselines. Across 16 target variables, we show that company growth exhibits a clear separation between trend-driven predictability and fluctuation-driven predictability, with their relative importance depending strongly on company size and volatility. Interpretability analyses further show that STIML captures multivariate dependencies beyond simple autocorrelation, and that macroeconomic variables contribute significantly less to predictive performance on average. Moreover, we find the scaling-based growth model overlooks asymmetric deviations, which instead contain the structured and learnable signals, suggesting a path to refine mechanistic models.

cs.CE↗

arXiv2026

Scaling Laws for Function Diversity and Specialization Across Socioeconomic and Biological Complex Systems

Function diversity, the range of tasks individuals perform, and specialization, the distribution of function abundances, are fundamental to complex adaptive systems. In the absence of overarching principles, these properties have appeared domain-specific. Here, we introduce an empirical framework and a mathematical model for the diversification and specialization of functions across disparate systems, including bacteria, federal agencies, universities, corporations, and cities. We find that the number of functions grows sublinearly with system size, with exponents from 0.35 to 0.57, consistent with Heaps' Law. In contrast, cities exhibit logarithmic scaling. To explain these empirical findings, we generalize the Yule-Simon model by introducing two key parameters: a diversification parameter that characterizes how existing functions inhibit the creation of new ones, and a specialization parameter that describes how a function's attractiveness depends on its abundance. Our model enables cross-system comparisons, from microorganisms to metropolitan areas. The analysis suggests that what drives the creation of new functions depends on the system's goals and structure: federal agencies tend to ensure comprehensive coverage of necessary functions; cities tend to slow the creation of new occupations as existing ones expand; and cells occupy an intermediate position. Once functions are introduced, their growth follows a remarkably universal pattern across all systems.

physics.soc-ph↗

arXiv2025

Spatial Patterning and Selection: How the Environment Shapes Molecular Complexity

Assembly theory predicts that a distinguishing signature of life is its ability to produce complex molecules in abundance, opening new possibilities for life detection. Experimental validation of this approach has so far relied on abiotic controls like meteoritic material, or simple, well-mixed chemical systems. However, decades of research in self-organization have shown that spatial patterning can foster dynamical self-organization. This raises the possibility that systems with nontrivial spatial patterns might promote abiotic formation of molecules with higher than expected assembly indices, potentially leading to false positives in life detection approaches based on assembly theory. To explore this, we used a model of artificial chemistry to investigate how spatial organization can influence the development of molecular assembly indices. Our findings reveal that transport factors, such as diffusion, significantly affect the distribution of chemical species within a system. Additionally, system topology critically impacts the distribution of assembly indices: while it does not enable arbitrary complexity, ordered lattices can shift the threshold for abiotic chemistry upward. Moreover, we demonstrate that diffusion can impede the formation and detection of these high assembly index molecules, bearing important implications for life detection experiments and astrobiological missions.

physics.bio-ph↗

arXiv2025

The impact of strong activity disruption on building energetics

Evidence shows that biological organisms tend to be more energetically efficient per unit size. These scaling patterns observed in biological organisms have also been observed in the energetic requirements of cities. However, at lower levels of organization where energetic interventions can be more manageable, such as buildings, this analysis has remained more elusive due to the difficulties in collecting fine-grained data. Here, we use the maintenance energy usage in buildings at the Massachusetts Institute of Technology (MIT) from 2009 to 2024 to analyze energetic trends at the scale of individual buildings and their sensitivity to strong external perturbations. We find that, similar to the baseline metabolism of biological organisms, large buildings are on average $24\%$ more energetically efficient per unit size than smaller buildings. Because it has become debatable how to better measure the efficiency of buildings, this scaling pattern naturally establishes a baseline efficiency for buildings, where deviations from the mean would imply a more or less efficient building than the baseline according to volume. This relative efficiency progressively increased to $34\%$ until 2020. However, the strong activity disruption caused by the COVID-19 pandemic acted as a major shock, removing this trend and leading to a reversal to the expected $24\%$ baseline level. This suggests that energetic adaptations are contingent on relatively stable conditions.

physics.soc-ph↗

arXiv2025

How much regulation do we need from genomes to society?

Regulatory functions are essential in both socioeconomic and biological systems, from corporate managers to regulatory genes. Regulatory functions come with substantial costs and benefits, and the balance of the two is often taken for granted. A fundamental question for all complex systems becomes how much regulatory function do they need for their size and function? Here, we present empirical evidence that regulatory functions scale systematically across diverse systems: biological organisms (bacterial and eukaryotic genomes), human organizations (companies, federal agencies, universities), and decentralized entities (Wikipedia, cities). We combine an analysis of large data sets from each of these domains with a simple conceptual model. The model predicts that the scaling of regulatory costs shifts with system structure. Well-mixed small systems exhibit superlinear scaling between size and regulatory function, while modular large ones show sublinear or linear scaling, both in agreement with data. Finally, we find that socioeconomic systems that contain more diverse occupational functions tend to have more regulatory costs than expected from the scaling relationships, confirming the hypothesis that the type and complexity of interactions also play a role in regulatory costs. Our cross-system comparison offers a mechanistic framework for understanding regulatory function and can potentially guide efforts to analyze the costs and benefits of regulatory function in diverse systems.

nlin.AO↗

arXiv2025

Synthesis of innovation and obsolescence

Innovation and obsolescence describe the dynamics of ever-churning social and biological systems, from the development of economic markets to scientific and technological progress to biological evolution. They have been widely discussed, but in isolation, leading to fragmented modeling of their dynamics. This poses a problem for connecting and building on what we know about their shared mechanisms. Here we collectively propose a conceptual and mathematical framework to transcend field boundaries and to explore unifying theoretical frameworks and open challenges. We ring an optimistic note for weaving together disparate threads with key ideas from the wide and largely disconnected literature by focusing on the duality of innovation and obsolescence and by proposing a mathematical framework to unify the metaphors between constitutive elements.

physics.soc-ph↗

arXiv2025

Bioenergetic trophic trade-offs determine mass-dependent extinction thresholds across the Cenozoic

Body size drives the energetic demands of organisms, constraining trophic interactions between species and playing a significant role in shaping the feasibility of species' populations in a community. On macroevolutionary timescales, these demands feed back to shape the selective landscape driving the evolution of body size and diet. We develop a theoretical framework for a three-level trophic food chain -- typical for terrestrial mammalian ecosystems -- premised on bioenergetic trade-offs to explore mammalian population dynamics. Our results show that interactions between predators, prey, and external subsidies generate instabilities linked to body size extrema, corresponding to observed limits of predator size and diet. These instabilities generate size-dependent constraints on coexistence and highlight a feasibility range for carnivore size between 40 to 110 kg, encompassing the mean body size of terrestrial Cenozoic hypercarnivores. Finally, we show that predator dietary generalization confers a selective advantage to larger carnivores, which then declines at megapredator body sizes, aligning with diet breadth estimates for contemporary and Pleistocene species. Our framework underscores the importance of understanding macroevolutionary constraints through the lens of ecological pressures, where the selective forces shaping and reshaping the dynamics of communities can be explored.

q-bio.PE↗

arXiv2024

Assembly Theory and its Relationship with Computational Complexity

Assembly theory (AT) quantifies selection using the assembly equation and identifies complex objects that occur in abundance based on two measurements, assembly index and copy number, where the assembly index is the minimum number of joining operations necessary to construct an object from basic parts, and the copy number is how many instances of the given object(s) are observed. Together these define a quantity, called Assembly, which captures the amount of causation required to produce objects in abundance in an observed sample. This contrasts with the random generation of objects. Herein we describe how AT's focus on selection as the mechanism for generating complexity offers a distinct approach, and answers different questions, than computational complexity theory with its focus on minimum descriptions via compressibility. To explore formal differences between the two approaches, we show several simple and explicit mathematical examples demonstrating that the assembly index, itself only one piece of the theoretical framework of AT, is formally not equivalent to other commonly used complexity measures from computer science and information theory including Shannon entropy, Huffman encoding, and Lempel-Ziv-Welch compression. We also include proofs that assembly index is not in the same computational complexity class as these compression algorithms and discuss fundamental differences in the ontological basis of AT, and assembly index as a physical observable, which distinguish it from theoretical approaches to formalizing life that are unmoored from measurement.

cs.CC↗

arXiv2024

Work extraction with feedback control using limited resources

Many physical, biological, and even social systems are faced with the problem of how to efficiently harvest free energy from an environment that can have many possible states, yet only have a limited number of harvesting protocols to choose among. We investigate this scenario by extending earlier work on using feedback control to extract work from nonequilibirum systems. Specifically, in contrast to that previous work on the thermodynamics of feedback control, we analyze the combined and separate effects of noisy measurements, memory limitations, and limitations on the number of possible work extraction protocols. Our analysis provides a general recipe to construct repertoires of allowed harvesting protocols that minimize the expected thermodynamic losses during free energy harvesting, i.e., that minimize expected entropy production. In particular, our results highlight that the benefits of feedback control over uninformed (random) actions extend beyond just the associated information gain, often by many orders of magnitude. Our results also uncover the effects of limitations on the number of possible harvesting protocols when there is uncertainty about the distribution over states of the environment.

cond-mat.stat-mech↗

arXiv2024

Spatial Structure Supports Diversity in Prebiotic Autocatalytic Chemical Ecosystems

Autocatalysis is thought to have played an important role in the earliest stages of the origin of life. An autocatalytic cycle (AC) is a set of reactions that results in stoichiometric increase in its constituent chemicals. When the reactions of multiple interacting ACs are active in a region of space, they can have interactions analogous to those between species in biological ecosystems. Prior studies of autocatalytic chemical ecosystems (ACEs) have suggested avenues for accumulating complexity, such as ecological succession, as well as obstacles such as competitive exclusion. We extend this ecological framework to investigate the effects of surface adsorption, desorption, and diffusion on ACE ecology. Simulating ACEs as particle-based stochastic reaction-diffusion systems in spatial environments-including open, two-dimensional reaction-diffusion systems and adsorptive mineral surfaces-we demonstrate that spatial structure can enhance ACE diversity by i) permitting otherwise mutually exclusive ACs to coexist and ii) subjecting new AC traits to selection.

q-bio.PE↗

arXiv2023

Metabolic scaling in small life forms

Metabolic scaling is one of the most important patterns in biology. Theory explaining the 3/4-power size-scaling of biological metabolic rate does not predict the non-linear scaling observed for smaller life forms. Here we present a new model for cells $<10^{-8}$ m$^{3}$ that maximizes power from the reaction-displacement dynamics of enzyme-catalyzed reactions. Maximum metabolic rate is achieved through an allocation of cell volume to optimize a ratio of reaction velocity to molecular movement. Small cells $< 10^{-17}$ m$^{3}$ generate power under diffusion by diluting enzyme concentration as cell volume increases. Larger cells require bulk flow of cytoplasm generated by molecular motors. These outcomes predict curves with literature-reported parameters that match the observed scaling of metabolic rates for unicells, and predicts the volume at which Prokaryotes transition to Eukaryotes. We thus reveal multiple size-dependent physical constraints for microbes in a model that extends prior work to provide a parsimonious hypothesis for how metabolism scales across small life.

physics.bio-ph↗

arXiv2023

On the dynamics of mortality and the ephemeral nature of mammalian megafauna

Energy flow through consumer-resource interactions is largely determined by body size. Allometric relationships govern the dynamics of populations by impacting rates of reproduction, as well as alternative sources of mortality, which have differential impacts on smaller to larger organisms. Here we derive and investigate the timescales associated with four alternative sources of mortality for terrestrial mammals: mortality from starvation, mortality associated with aging, mortality from consumption by predators, and mortality introduced by anthropogenic subsidized harvest. The incorporation of these allometric relationships into a minimal consumer-resource model illuminates central constraints that may contribute to the structure of mammalian communities. Our framework reveals that while starvation largely impacts smaller-bodied species, the allometry of senescence is expected to be more difficult to observe. In contrast, external predation and subsidized harvest have greater impacts on the populations of larger-bodied species. Moreover, the inclusion of predation mortality reveals mass thresholds for mammalian herbivores, where dynamic instabilities may limit the feasibility of megafaunal populations. We show how these thresholds vary with alternative predator-prey mass relationships, which are not well understood within terrestrial systems. Finally, we use our framework to predict the harvest pressure required to induce mass-specific extinctions, which closely align with previous estimates of anthropogenic megafaunal exploitation in both paleontological and historical contexts. Together our results underscore the tenuous nature of megafaunal populations, and how different sources of mortality may contribute to their ephemeral nature over evolutionary time.

q-bio.PE↗

arXiv2023

Assembly Theory Explains and Quantifies the Emergence of Selection and Evolution

Since the time of Darwin, scientists have struggled to reconcile the evolution of biological forms in a universe determined by fixed laws. These laws underpin the origin of life, evolution, human culture and technology, as set by the boundary conditions of the universe, however these laws cannot predict the emergence of these things. By contrast evolutionary theory works in the opposite direction, indicating how selection can explain why some things exist and not others. To understand how open-ended forms can emerge in a forward-process from physics that does not include their design, a new approach to understand the non-biological to biological transition is necessary. Herein, we present a new theory, Assembly Theory (AT), which explains and quantifies the emergence of selection and evolution. In AT, the complexity of an individual observable object is measured by its Assembly Index (a), defined as the minimal number of steps needed to construct the object from basic building blocks. Combining a with the copy number defines a new quantity called Assembly which quantifies the amount of selection required to produce a given ensemble of objects. We investigate the internal structure and properties of assembly space and quantify the dynamics of undirected exploratory processes as compared to the directed processes that emerge from selection. The implementation of assembly theory allows the emergence of selection in physical systems to be quantified at any scale as the transition from undirected-discovery dynamics to a selected process within the assembly space. This yields a mechanism for the onset of selection and evolution and a formal approach to defining life. Because the assembly of an object is easily calculable and measurable it is possible to quantify a lower limit on the amount of selection and memory required to produce complexity uniquely linked to biology in the universe.

physics.bio-ph↗

arXiv2022

Idea engines: Unifying innovation and obsolescence from markets and genetic evolution to science

Innovation and obsolescence describe dynamics of ever-churning and adapting social and biological systems, concepts that encompass field-specific formulations. We formalize the connection with a reduced model of the dynamics of the "space of the possible" (e.g. technologies, mutations, theories) to which agents (e.g. firms, organisms, scientists) couple as they grow, die, and replicate. We predict three regimes: the space is finite, ever growing, or a Schumpeterian dystopia in which obsolescence drives the system to collapse. We reveal a critical boundary at which the space of the possible fluctuates dramatically in size, displaying recurrent periods of minimal and of veritable diversity. When the space is finite, corresponding to physically realizable systems, we find surprising structure. This structure predicts a taxonomy for the density of agents near and away from the innovative frontier that we compare with distributions of firm productivity, covid diversity, and citation rates for scientific publications. Remarkably, our minimal model derived from first principles aligns with empirical examples, implying a follow-the-leader dynamic in firm cost efficiency and biological evolution, whereas scientific progress reflects consensus that waits on old ideas to go obsolete. Our theory introduces a fresh and empirically testable framework for unifying innovation and obsolescence across fields.

physics.soc-ph↗

arXiv2022

Worldwide scaling of waste generation in urban systems

The production of waste as a consequence of human activities is one of the most fundamental challenges facing our society and global ecological systems. Waste generation is rapidly increasing, with corresponding shifts in the structure of our societies where almost all nations are moving from rural agrarian societies to urban and technological ones. However, the connections between these radical societal shifts and waste generation have not yet been described. Here we apply scaling theory to establish a new understanding of waste in urban systems. We identify universal scaling laws of waste generation across diverse urban systems worldwide for three forms of waste: wastewater, municipal solid waste, and greenhouse gasses. We show that wastewater generation scales superlinearly, municipal solid waste scales linearly, and greenhouse gasses scales sublinearly with city size. In specific cases production can be understood in terms of city size coupled with financial and natural resources. For example, wastewater generation can be understood in terms of the increased economic activity of larger cities, and the deviations around the scaling relationship - indicating relative efficiency - depend on GDP per person and local rainfall. We also show how the temporal evolution of these scaling relationships reveals a loss of economies of scale and the general increase in waste production, where sublinear scaling relationships become linear. Our findings suggest general mechanisms controlling waste generation across diverse cities and global urban systems. Our approach offers a systematic approach to uncover these underlying mechanisms that might be key to reducing waste and pursing a more sustainable future.

physics.soc-ph↗