Thermodynamics of exponential Kolmogorov-Nagumo averages

This paper investigates generalized thermodynamic relationships in physical systems where relevant macroscopic variables are determined by the exponential Kolmogorov-Nagumo average. We show that while the thermodynamic entropy of such systems is naturally described by R\'{e}nyi's entropy with parameter $\gamma$, their statistics under equilibrium thermodynamics are still described by an ordinary Boltzmann distribution, which can be interpreted as a system with inverse temperature $\beta$ quenched to another heat bath with inverse temperature $\beta' = (1-\gamma)\beta$. For the non-equilibrium case, we show how the dynamics of systems described by exponential Kolmogorov-Nagumo averages still observe a second law of thermodynamics and H-theorem. We further discuss the applications of stochastic thermodynamics in those systems - namely, the validity of fluctuation theorems - and the connection with thermodynamic length.Comment: 12 pages, 1 table. arXiv admin note: text overlap with arXiv:2203.1367

Using information theory to measure the emergence of artificial free will in a spiking brain-constrained model of the human cortex

Cell Assembly (CA) circuits are known to emerge in neurocomputational models as a result of Hebbian-like learning. Intriguingly, when a brain-like architecture is used, CAs spontaneously "ignite" in absence of any stimulus, and the patterns of network activation occurring during such ignitions closely match those observed in the human brain during non-stimulus driven, endogenous decisions to act [1]. This suggests that sub-threshold reverberation of noise within CA circuits (which drives their ignition) may be a possible mechanism underlying seemingly "free" and volitional (yet possibly pre-consciously determined) action decisions [2]. It is unclear, however, whether such spontaneous CA ignitions are truly an emergent property of the brain-like model, or whether they are somehow "pre-encoded" in the system's features. Can we provide objective evidence supporting (or falsifying) the hypothesis that these spontaneous events are de facto non pre-determined and can be thus be considered as the network's own endogenous "action decisions"? To investigate this issue, we used a spiking brain-constrained model of six cortical areas and, after replicating the previously documented CA emergence and spontaneous ignitions in it, we analysed its emergent properties using information theoretic measures. Recent techniques in information theory allow quantifying emergence in complex systems (including the brain) [3]. Here, we applied these measures to test for the presence of emergence during spontaneous, unprovoked CA circuit ignition. Specifically, we analysed the different modalities of emergence associated with cell assembly ignition and lifecycle (downward causation and causal decoupling). Preliminary results show the highest levels of emergent behaviour (specifically, causal decoupling) during cell assembly ignition, which gradually fade as CA activation dissipates. Such increased levels of causal decoupling observed during (and prior to) CA ignition episodes confirm the presence of an emergent feature in the neural model. In summary, we present here the application of formal criteria used for determining the presence of emergence in complex systems to a spiking, brain-constrained neurocomputational model of the cortex that can mechanistically explain the neural origins of so-called "free", volitional action decisions. Initial results of the information-theoretical analysis indicate that spontaneous CA circuit ignitions, driven by reverberation of noise within them, truly constitute an emergent feature of the brain-like architecture, suggesting that this phenomenon should be considered as an endogenous (i.e., internally generated, and not pre-determined) feature of the artificial neural network. References: [1] Garagnani, M. & Pulvermüller, F. (2013) Neuronal correlates of decisions to speak and act: spontaneous emergence and dynamic topographies in a computational model of frontal and temporal areas. Brain and Language 127(1):75–85. [2] Schurger A, Mylopoulos M, Rosenthal D. (2016) Neural antecedents of spontaneous voluntary movement: a new perspective. Trends in Cognitive Sciences. 20(2), 77-79. [3] Rosas F.E., Mediano P.A.M., Jensen H.J., Seth A.K., Barrett A.B., Carhart-Harris R.L., et al. (2020) Reconciling emergences: An informationtheoretic approach to identify causal emergence in multivariate data. PLoS Comput Biol 16(12): e1008289

Dynamical noise can enhance high-order statistical structure in complex systems

Recent research has provided a wealth of evidence highlighting the pivotal role of high-order interdependencies in supporting the information-processing capabilities of distributed complex systems. These findings may suggest that high-order interdependencies constitute a powerful resource that is, however, challenging to harness and can be readily disrupted. In this paper we contest this perspective by demonstrating that high-order interdependencies can not only exhibit robustness to stochastic perturbations, but can in fact be enhanced by them. Using elementary cellular automata as a general testbed, our results unveil the capacity of dynamical noise to enhance the statistical regularities between agents and, intriguingly, even alter the prevailing character of their interdependencies. Furthermore, our results show that these effects are related to the high-order structure of the local rules, which affect the system's susceptibility to noise and characteristic times-scales. These results deepen our understanding of how high-order interdependencies may spontaneously emerge within distributed systems interacting with stochastic environments, thus providing an initial step towards elucidating their origin and function in complex systems like the human brain.Comment: 8 pages, 4 figures, 2 table

Nested Selves: Self-Organization and Shared Markov Blankets in Prenatal Development in Humans

The immune system is a central component of organismic function in humans. This paper addresses self-organization of biological systems in relation to-and nested within-other biological systems in pregnancy. Pregnancy constitutes a fundamental state for human embodiment and a key step in the evolution and conservation of our species. While not all humans can be pregnant, our initial state of emerging and growing within another person's body is universal. Hence, the pregnant state does not concern some individuals but all individuals. Indeed, the hierarchical relationship in pregnancy reflects an even earlier autopoietic process in the embryo by which the number of individuals in a single blastoderm is dynamically determined by cell- interactions. The relationship and the interactions between the two self-organizing systems during pregnancy may play a pivotal role in understanding the nature of biological self-organization per se in humans. Specifically, we consider the role of the immune system in biological self-organization in addition to neural/brain systems that furnish us with a sense of self. We examine the complex case of pregnancy, whereby two immune systems need to negotiate the exchange of resources and information in order to maintain viable self-regulation of nested systems. We conclude with a proposal for the mechanisms-that scaffold the complex relationship between two self-organising systems in pregnancy-through the lens of the Active Inference, with a focus on shared Markov blankets