Last year, John Hopfield and Geoffrey Hinton received the Nobel Prize in Physics for developing statistical physics-based neural network models for machine learning and artificial intelligence (AI). The vertiginous growth of AI applications has reached all societal corners, there is no field left untouched by the benefits of AI [1]. The computer scientist John McCarthy coined the term in the 50s stating “Every aspect of learning or any other feature of intelligence can in principle be so precisely described that a machine can be made to simulate it.” The foundations of AI lie in cybernetics (kybernetiké in Greek, the art of guiding), a term coined by the physicist André-Marie Ampere in his classification of sciences of 1834. Work on cybernetics and feedback, a branch of science introduced by Norbert Wiener in 1948, together with developments in information theory and automated systems, gave the kick-off to the good old-fashioned AI, where basic symbols such as words or pictures are the bricks to build up higher-order symbolic structures. The incapability of symbolic AI to evolve and learn led to a stall in the 80s without further progress.

The AI of today would not have seen the light were it not for the foundational contributions of Hopfield and Hinton, who introduced in the 80s statistical-physics-based models for artificial neural networks (ANNs) and Boltzmann machines (BMs). Together with the ever-growing amount of available data, these ideas have revolutionized how we analyze and build algorithms to make predictions unforeseeable decades ago. Built upon developments in spin-glass theory and complexity (awarded the Nobel Prize in Physics 2021 to G. Parisi), ANNs and BMs introduce connectionism and statistics-based inference methods (machine learning) to dynamically evolve the internal structure of trainable networks containing visible and hidden units [2]. The nodes and links of such networks contain representations of informational structures and 3D objects, such as images, speech and language. The capability of such networks and representations to evolve and learn makes them reminiscent of how biological brains work, bringing artificial prediction machines closer to human intelligence and consciousness.

In this issue, selected contributions from experts in the fields of statistical physics, machine learning, networks, and particle accelerators offer a glimpse of the fundamental advances in physics and science triggered by the discoveries of Hopfield, Hinton, and co-workers. Their ideas built on the energy-information landscape paradigm. While associative memory in an energy landscape was quintessential to the Hopfield model, the introduction of hidden layers of information has been key in building probabilistic Boltzmann machines. AI’s predictive power is mainly determined by the information content encoded in the data representation of the network. However, as Landauer showed in the 60s, information is physical, and the erasure of one bit produces at least the heat equivalent of kBTlog2 (~10^-21 Joules at 25°C). A single living cell, or even the human brain, requires large amounts of energy to operate, mostly dissipated in the form of heat. Understanding how living matter works brings AI close to artificial life (ALife) or the construction of sustainable self-replicating systems resembling living beings [1]. It is no coincidence that the Nobel Prize in Chemistry 2024 was also awarded to related AI developments in protein structure prediction and design. Protein folding is an exothermic reaction, which energetics cannot be described by “folding rules”. Despite life processes are intrinsically dissipative, the relationship between energy and information remains obscure, a problem AI will face sooner or later.

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© European Physical Society, EDP Sciences, 2025