In recent years, advances in science, technology, and the way in which we view our world have led to anincreasingly broad use of the term “intelligence”. As we learn more about biological systems, we find more and more examples of complex and precise adaptive behavior in animals and plants. Similarly, as we build more complex computational systems, we recognize the emergence of highly sophisticated structures capable of solving increasingly complex problems. These behaviors show characteristics in common with the sort of complex behaviors and learning capabilities we find in humans, and therefore it is common to see them referred to as “intelligent”. These analogies are problematic as the term "intelligence" is inextricably associated with human-like capabilities. While these issues have been discussed by leading researchers of AI and renowned psychologists and biologists highlighting the commonalities and differences between AI and biological intelligence, there have been few rigorous attempts to create an interdisciplinary approach to the modern problem of intelligence. This article proposes a comparative framework to discuss what we call “purposeful behavior”, a characteristic shared by systems capable of gathering and processing information from their surroundings and modifying their actions in order to fulfill a series of implicit or explicit goals. Our aim is twofold: on the one hand, the term purposeful behavior allows us to describe the behavior of these systems without using the term "intelligence", avoiding the comparison with human capabilities. On the other hand, we hope that our framework encourages interdisciplinary discussion to help advance our understanding of the relationships among different systems and their capabilities.

The Thermodynamic Formalism provides a rigorous mathematical framework to study quantitative and qualitative aspects of dynamical systems. At its core there is a variational principle and corresponding, in its simplest form, to the Maximum Entropy principle, used as a statistical inference procedure to represent, by specific probability measures (Gibbs measures), the collective behaviour of complex systems. This framework has found applications in different domains of scienThe Thermodynamic Formalism provides a rigorous mathematical framework to study quantitative and qualitative aspects of dynamical systems. At its core there is a variational principle and corresponding, in its simplest form, to the Maximum Entropy principle, used as a statistical inference procedure to represent, by specific probability measures (Gibbs measures), the collective behaviour of complex systems. This framework has found applications in different domains of science, in particular, has been fruitful and influential in neurosciences. In this article, we review how the Thermodynamic Formalism can be exploited in the field of theoretical neuroscience, as a conceptual and operational tool, to link the dynamics of interacting neurons and the statistics of action potentials from either experimental data or mathematical models. We comment on perspectives and open problems in theoretical neuroscience that could be addressed within this formalism.ce, in particular, has been fruitful and influential in neurosciences. In this article, we review how the Thermodynamic Formalism can be exploited in the field of theoretical neuroscience, as a conceptual and operational tool, to link the dynamics of interacting neurons and the statistics of action potentials from either experimental data or mathematical models. We comment on perspectives and open problems in theoretical neuroscience that could be addressed within this formalism.

We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful in this context to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.