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Foundations, Volume 5, Issue 3 (September 2025) – 2 articles

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19 pages, 342 KiB  
Article
Fisher Information in Helmholtz–Boltzmann Thermodynamics of Mechanical Systems
by Marco Favretti
Foundations 2025, 5(3), 24; https://doi.org/10.3390/foundations5030024 - 4 Jul 2025
Viewed by 152
Abstract
In this paper, we review Helmholtz–Boltzmann thermodynamics for mechanical systems depending on parameters, and we compute the Fisher information matrix for the associated probability density. The divergence of Fisher information has been used as a signal for the existence of phase transitions in [...] Read more.
In this paper, we review Helmholtz–Boltzmann thermodynamics for mechanical systems depending on parameters, and we compute the Fisher information matrix for the associated probability density. The divergence of Fisher information has been used as a signal for the existence of phase transitions in finite systems even in the absence of a thermodynamic limit. We investigate through examples if qualitative changes in the dynamic of mechanical systems described by Helmholtz–Boltzmann thermodynamic formalism can be detected using Fisher information. Full article
(This article belongs to the Section Physical Sciences)
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22 pages, 323 KiB  
Article
Mathematical Formalism and Physical Models for Generative Artificial Intelligence
by Zeqian Chen
Foundations 2025, 5(3), 23; https://doi.org/10.3390/foundations5030023 - 24 Jun 2025
Viewed by 244
Abstract
This paper presents a mathematical formalism for generative artificial intelligence (GAI). Our starting point is an observation that a “histories” approach to physical systems agrees with the compositional nature of deep neural networks. Mathematically, we define a GAI system as a family of [...] Read more.
This paper presents a mathematical formalism for generative artificial intelligence (GAI). Our starting point is an observation that a “histories” approach to physical systems agrees with the compositional nature of deep neural networks. Mathematically, we define a GAI system as a family of sequential joint probabilities associated with input texts and temporal sequences of tokens (as physical event histories). From a physical perspective on modern chips, we then construct physical models realizing GAI systems as open quantum systems. Finally, as an illustration, we construct physical models realizing large language models based on a transformer architecture as open quantum systems in the Fock space over the Hilbert space of tokens. Our physical models underlie the transformer architecture for large language models. Full article
(This article belongs to the Section Physical Sciences)
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