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Statistical Physics and Nonlinear Dynamics for Complex Systems

A Special Issue of Entropy (ISSN 1099-4300) belonging to the section "Statistical Physics".

Deadline for manuscript submissions: 31 October 2026 | Viewed by 1905

Editors


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Guest Editor
Instituto de Física, UNAM, Mexico City, Mexico
Interests: statistical physics; complex systems; nonlinear dynamics; transitions to chaos; critical fluctuations; localization transition; glassy dynamics; self-organization; rank distributions; allometric scaling

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Guest Editor
Instituto de Física, UNAM, Mexico City, Mexico
Interests: nonequilibrium statistical physics; stochastic processes in physics; collective phenomena; nonequilibrium quantum dynamics; quantum statistical physics

Special Issue Information

Dear Colleagues,

The mounting number of studies on complex systems in recent years is quickly consuming its initial empirical, heuristic stage and offering views of its next phenomenological stage, with predictive and comprehension qualities. From an exact sciences perspective, successful schemes have been developed based on statistical physics and nonlinear dynamical concepts. This Special Issue seeks to highlight innovative research based on the above-mentioned disciplines and concepts, offering new methods or the corroboration of phenomenological approaches to foresee and understand complex systems.

Topics of interest:

1. Basic notions, guiding concepts and core issues on complex systems

  • Demonstration of paradigms, edge of chaos, criticality and others.
  • Self-organization, including self-organized criticality.
  • Thermodynamic viewpoints of diversity, biological or others.

2. Insights into empirical laws found in complex systems

  • Rank distributions, including Zipf law.
  • Regularities in cosmological, geophysical and other structures.
  • Allometric scaling in biology and in human organizations.

3. Approaches and methods applied to the study complex systems

  • Game theory and evolutionary dynamics.
  • Self-similar and scale invariant network approaches.
  • Large numbers and large-scale order questions.

4.  Modeling of complex systems via condensed-matter physics concepts

  • Critical fluctuations applied to catastrophes and tipping points.
  • Glassy dynamics applied to traffic issues.
  • Localization or synchronization applied to collective behavior and foraging.

Prof. Dr. Alberto Robledo
Dr. Francisco J. Sevilla
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

  • dissipative processes
  • onset of chaos
  • borderline behaviors
  • self-organization
  • diversity
  • Zipf law
  • allometry
  • evolutionary game theory
  • time series into networks
  • urban dynamics
  • swarm intelligence.

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Published Papers (2 papers)

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Research

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24 pages, 3379 KB  
Article
Scaling Analysis of Seismic Ground Motion Signals
by Giuliana Paradiso, Federica Di Michele, Matteo Colangeli, Bruno Rubino and Lamberto Rondoni
Entropy 2026, 28(9), 972; https://doi.org/10.3390/e28090972 - 1 Sep 2026
Viewed by 211
Abstract
Earthquakes exhibit well-documented statistical regularities at the catalogue level, such as the Gutenberg–Richter magnitude–frequency relation and the Omori–Utsu aftershock decay, often interpreted as signatures of seismicity as a driven, dissipative system far from thermodynamic equilibrium. However, whether comparable signatures, such as scale invariance [...] Read more.
Earthquakes exhibit well-documented statistical regularities at the catalogue level, such as the Gutenberg–Richter magnitude–frequency relation and the Omori–Utsu aftershock decay, often interpreted as signatures of seismicity as a driven, dissipative system far from thermodynamic equilibrium. However, whether comparable signatures, such as scale invariance and anomalous diffusion, can be detected directly within individual ground motion recordings remains an open question. This work investigates whether acceleration, velocity, and displacement signals recorded during the 2009 Mw 6.1 L’Aquila earthquake display statistical properties consistent with non-equilibrium complex systems, and whether different seismic phases carry distinct, reproducible statistical signatures. P- and S-wave onset times are estimated using AR-AIC, with adaptive search windows centred on theoretical arrivals from the CRUST1.0 velocity model. Coda onset is determined using three complementary criteria combined into a median ensemble, enabling the segmentation of each recording into up to five temporal windows. Displacement moment scaling is analysed for each window and signal type, within the framework of strong anomalous diffusion, yielding the scaling exponents ζ(q). Robustness is systematically assessed against the choice of coda onset method, the empirical thresholds defining coda onset and end, the sub-interval of τ used in the moment scaling fit, and the filter band applied to the ground motion signals. Evidence for anomalous diffusion is nuanced: both its sign and magnitude depend on the seismic phase, with only a subset of configurations remaining stable across all segmentation schemes tested. These results indicate that anomalous scaling signatures, when present, are not universal, and that systematic robustness analyses are essential to distinguish genuine physical effects from segmentation artefacts. Full article
(This article belongs to the Special Issue Statistical Physics and Nonlinear Dynamics for Complex Systems)
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Review

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18 pages, 12188 KB  
Review
The Simplest Complexity: The Story of the Three-Body Problem
by Barak Kol
Entropy 2026, 28(6), 610; https://doi.org/10.3390/e28060610 - 29 May 2026
Viewed by 1279
Abstract
This article offers a broad-brush account of the Newtonian three-body problem, from its origins with Newton to its vibrant present, emphasizing its enduring influence on theoretical physics. It unfolds through a series of self-contained episodes that illuminate the scientific fields and the paradigm [...] Read more.
This article offers a broad-brush account of the Newtonian three-body problem, from its origins with Newton to its vibrant present, emphasizing its enduring influence on theoretical physics. It unfolds through a series of self-contained episodes that illuminate the scientific fields and the paradigm shift that have grown out of this problem. Full article
(This article belongs to the Special Issue Statistical Physics and Nonlinear Dynamics for Complex Systems)
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