Costolo, Michael

This paper introduces a constraint-limited model of combinatorial growth that examines how feasibility scales with increasing system dimensionality. The framework analyzes the balance between expanding possibility spaces and constraint structures that prune feasible configurations. The model shows that when feasible configurations grow as c^n within a combinatorial space of size 2^n, the feasible fraction collapses for constant c < 2. Sustained novelty generation therefore requires c(n) to approach the combinatorial base, producing a narrow “complexity corridor” between regimes of trivial repetition and combinatorial sparsity. The paper derives the analytic structure of this corridor and explores it through numerical simulations and visualizations. The results suggest a possible structural explanation for why complex systems may emerge only within a narrow range where combinatorial expansion and constraint relaxation operate at comparable scales.  The manuscript includes the full mathematical derivation, simulation results, and discussion of implications for complex systems.

Read the full article at: zenodo.org

How and why do complex chemical and biological systems self-organize into ordered states far from thermodynamic equilibrium? Despite advances in thermodynamics, kinetics, and information theory, a unifying principle that links organization and efficiency across scales has remained elusive. In open systems, productive-event trajectories are conditioned on starting at a source and ending at a sink. This work proposes a stochastic–dissipative least-action triad framework in which (i) a path-ensemble weighting biases trajectories by their action cost, (ii) feedback processes sharpen this distribution, and (iii) the ensemble evolves toward a least-average-action attractor, decreasing during self-organization and increasing during decay. A parametric cross-scale metric—Average Action Efficiency (AAE)—is defined, which is inversely proportional to the average action per productive event. Under reinforcing feedback, identities derived from the exponential-family path measure show that the average action decreases and AAE rises monotonically. In future extensions, this formulation could help bridge quantum, classical, and biological regimes while remaining computationally tractable, because its empirical version relies on aggregate energetic and timing data rather than enumerating individual trajectories. AAE reaches a local maximum at a non-equilibrium steady state under fixed operational context, consistent with the present formulation, and connections to thermodynamic and informational measures are made. A companion article (Part II) details empirical estimation strategies and applications (Georgiev, 2025a).

Georgi Yordanov Georgiev

BioSystems

Volume 262, April 2026, 105647

Read the full article at: www.sciencedirect.com

See Also: Part II: Empirical estimation, Average Action Efficiency, and applications to ATP synthase

Junhua Yuan 
Nature Physics (2026)

Spontaneous switching between active and inactive states in bacterial chemosensory arrays is shown to operate near a critical point. Through biologically controlled disorder, cells balance high signal gain with fast response.

Read the full article at: www.nature.com

Viktor Stojkoski, César A. Hidalgo

Research Policy Volume 55, Issue 4, May 2026, 105454

Efforts to apply economic complexity to identify diversification opportunities often rely on diagrams comparing the relatedness and complexity of products, technologies, or industries. Yet, the use of these diagrams, is not based on empirical or theoretical evidence supporting some notion of optimality. Here, we introduce an optimization-based framework that identifies diversification opportunities by minimizing a cost function capturing the constraints imposed by an economy’s pattern of specialization. We show that the resulting portfolios often differ from those implied by relatedness–complexity diagrams, providing a target-oriented optimization layer to the economic complexity toolkit.

Read the full article at: www.sciencedirect.com

Erik Hoel
Scientific theories of consciousness should be falsifiable and non-trivial. Recent research has given us formal tools to analyze these requirements of falsifiability and non-triviality for theories of consciousness. Surprisingly, many contemporary theories of consciousness fail to pass this bar, including theories based on causal structure but also (as I demonstrate) theories based on function. Herein, I show these requirements of falsifiability and non-triviality especially constrain the potential consciousness of contemporary Large Language Models (LLMs) because of their proximity to systems that are equivalent to LLMs in terms of input/output function; yet, for these functionally equivalent systems, there cannot be any falsifiable and non-trivial theory of consciousness that judges them conscious. This forms the basis of a disproof of contemporary LLM consciousness. I then show a positive result, which is that theories of consciousness based on (or requiring) continual learning do satisfy the stringent formal constraints for a theory of consciousness in humans. Intriguingly, this work supports a hypothesis: If continual learning is linked to consciousness in humans, the current limitations of LLMs (which do not continually learn) are intimately tied to their lack of consciousness.

Read the full article at: arxiv.org