Geometric Perspectives in Emergent Phenomena: From Phase Transitions to Machine Learning
A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".
Deadline for manuscript submissions: 1 November 2026 | Viewed by 1509
Editors
Interests: phase transitions in microcanonical ensemble; collective phenomena; geometric approach to phase transition; topological defects
2. INFN Sezione di Perugia, 06123 Perugia, Italy
Interests: statistical mechanics; equilibrium phase-transitions; microcanonical ensemble; entanglement measure; quantum information
Special Issue Information
Dear Colleagues,
The notion of a phase transition has long served as a unifying framework for understanding collective phenomena in nature. From the magnetization of spin systems to the onset of superfluidity and superconductivity, critical phenomena have demonstrated how macroscopic order can emerge from simple microscopic interactions. Traditionally, such transitions have been analyzed within the paradigms of statistical mechanics and renormalization group theory, which highlight the thermodynamic limit and universality underlying scaling behaviors.
In recent years, however, two developments have profoundly reshaped our perspective on critical phenomena. On the one hand, geometric approaches—ranging from microcanonical entropy geometry and curvature flows to information geometry—have highlighted the deep role of underlying manifolds and energy landscapes. These methods suggest that thermodynamic behavior is already encoded in the geometry of energy level sets, and that curvature or entropic flows may serve as universal indicators of transitions, even in finite or non-equilibrium systems.
On the other hand, artificial intelligence and complex networks have become fertile domains where ideas of criticality and phase transitions reappear in unexpected forms. Neural networks, for instance, exhibit collective dynamics reminiscent of spin systems, while the emergence of coordinated behavior during learning often traverses critical regimes that can be characterized using analytical tools borrowed from statistical physics.
This Special Issue aims to bring together these threads, exploring the interplay of phase transitions, geometry, and artificial intelligence across classical, quantum, and artificial systems. Contributions may address, among other topics, the following:
- Classical and quantum phase transitions in many-body systems, with an emphasis on geometric and entropic perspectives;
- Geometric formulations of thermodynamics, including information geometry, entropy curvature, and emergent manifold structures;
- Signatures of criticality in machine learning and neural networks, from training dynamics to network connectivity;
- Cross-disciplinary methods, where AI assists in detecting or characterizing phase transitions, and physics provides a conceptual framework to understand learning processes.
By bridging communities traditionally separated—statistical physics, quantum technologies, geometry, and artificial intelligence—this Special Issue seeks to highlight critical phenomena as a universal language. Whether in condensed matter, quantum simulators, or neural networks, the emergence of order out of complexity reflects a common principle: geometry and criticality shape the dynamics of both natural and artificial systems.
We invite researchers from across these domains to contribute to this Special Issue, with the hope that this collection will stimulate dialogue and uncover new connections between physics, geometry, and intelligence.
Dr. Loris Di Cairano
Dr. Roberto Franzosi
Guest Editors
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
Keywords
- classical and quantum phase transitions (Ising, XY, quantum simulators, long-range models, BKT, etc.)
- geometric approaches (microcanonical geometry, entropy curvature, information geometry, geometric deep learning)
- artificial intelligence and complex networks (neural networks as spin systems, phase transitions in learning dynamics, criticality in AI models)
- cross-fertilization: exploiting AI to detect phase transition/exploiting statistical physics to understand neural networks
Benefits of Publishing in a Special Issue
- Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
- Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
- Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
- External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
- Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.
Further information on MDPI's Special Issue policies can be found here.
