Liquid neural networks (or ‘liquid brains’) are a widespread class of cognitive living networks characterized by a common feature: the agents (ants or immune cells, for example) move in space. Thus, no fixed, long-term agent-agent connections are maintained, in contrast with standard neural systems. How is this class of systems capable of displaying cognitive abilities, from learning to decision-making? In this paper, the collective dynamics, memory and learning properties of liquid brains is explored under the perspective of statistical physics. Using a comparative approach, we review the generic properties of three large classes of systems, namely: standard neural networks (solid brains), ant colonies and the immune system. It is shown that, despite their intrinsic physical differences, these systems share key properties with standard neural systems in terms of formal descriptions, but strongly depart in other ways. On one hand, the attractors found in liquid brains are not always based on connection weights but instead on population abundances. However, some liquid systems use fluctuations in ways similar to those found in cortical networks, suggesting a relevant role for criticality as a way of rapidly reacting to external signals. This article is part of the theme issue ‘Liquid brains, solid brains: How distributed cognitive architectures process information’.

We explore the application of a theory of semantic information to the well-motivated problem of resource foraging. Semantic information is defined as the subset of correlations, which is here measured via the transfer entropy, between agent $A$ and environment $E$ that is necessary for the agent to maintain its viability $V$. Viability, in turn, is endogenously defined as opposed to the use of exogenous quantities like utility functions. In our model, the forager's movements are determined by its ability to measure, via a sensor, the presence of an individual unit of resource, while the viability function is its expected lifetime. Through “interventions”—scrambling the correlations between agent and environment by noising the sensor—we demonstrate the presence of a critical value of the noise parameter, ${\eta }_c$, above which the forager's expected lifetime is dramatically reduced. On the other hand, for $\eta <{\eta }_c$ there is little to no effect on its ability to survive. We refer to this boundary as the semantic threshold, quantifying the subset of agent-environment correlations that the agent actually needs to maintain its desired state of staying alive. Each bit of information affects the agent's ability to persist both above and below the semantic threshold. Modeling the viability curve and its semantic threshold via forager and/or environment parameters, we show how the correlations are instantiated. Our work demonstrates the successful application of semantic information to a well-known agent-based model of biological and ecological interest. Additionally, we demonstrate that the concept of semantic thresholds may prove useful for understanding the role information plays in allowing systems to become autonomous agents.

Harvesting free energy from the environment is essential for the operation of many biological and artificial systems. We use techniques from stochastic thermodynamics to investigate the maximum rate of harvesting achievable by optimizing a set of reactions in a Markovian system, possibly under various kinds of topological, kinetic, and thermodynamic constraints. This question is relevant for the optimal design of new harvesting devices as well as for quantifying the efficiency of existing systems. We first demonstrate that the maximum harvesting rate can be expressed as a constrained convex optimization problem. We illustrate it on bacteriorhodopsin, a light-driven proton pump from Archaea, which we find is close to optimal under realistic conditions. In our second result, we solve the optimization problem in closed-form in three physically meaningful limiting regimes. These closed-form solutions are illustrated on two idealized models of unicyclic harvesting systems. Published by the American Physical Society 2024

Life evolved on our planet by means of a combination of Darwinian selection and innovations leading to higher levels of complexity. The emergence and selection of replicating entities is a central problem in prebiotic evolution. Theoretical models have shown how populations of different types of replicating entities exclude or coexist with other classes of replicators. Models are typically kinetic, based on standard replicator equations. On the other hand, the presence of thermodynamical constraints for these systems remain an open question. This is largely due to the lack of a general theory of statistical methods for systems far from equilibrium. Nonetheless, a first approach to this problem has been put forward in a series of novel developements falling under the rubric of the extended second law of thermodynamics. The work presented here is twofold: firstly, we review this theoretical framework and provide a brief description of the three fundamental replicator types in prebiotic evolution: parabolic, malthusian and hyperbolic. Secondly, we employ these previously mentioned techinques to explore how replicators are constrained by thermodynamics. Finally, we comment and discuss where further research should be focused on.

Cooperative interactions pervade in a broad range of many-body populations, such as ecological communities, social organizations, and economic webs. We investigate the dynamics of a population of two equivalent species A and B that are driven by cooperative and symmetric interactions between these species. For an isolated population, we determine the probability to reach fixation, where only one species remains, as a function of the initial concentrations of the two species, as well as the time to reach fixation. The latter scales exponentially with the population size. When members of each species migrate into the population at rate λ and replace a randomly selected individual, surprisingly rich dynamics ensues. Ostensibly, the population reaches a steady state, but the steady-state population distribution undergoes a unimodal to trimodal transition as the migration rate decreases below a critical value λ _c. In the low-migration regime, λ < λ _c, the steady state is not truly steady, but instead strongly fluctuates between near-fixation states, where the population consists of mostly A’s or of mostly B’s. The characteristic time scale of these fluctuations diverges as λ ⁻¹. Thus in spite of the cooperative interaction, a typical snapshot of the population will contain almost all A’s or almost all B’s.