Physics Reports最新文献

{"title":"Information theory for complex systems scientists: What, why, and how","authors":"Thomas F. Varley","doi":"10.1016/j.physrep.2025.09.007","DOIUrl":"10.1016/j.physrep.2025.09.007","url":null,"abstract":"<div><div>In the 21st century, many of the crucial scientific and technical issues facing humanity can be understood as problems associated with understanding, modeling, and ultimately controlling <em>complex systems</em>: systems comprised of a large number of non-trivially interacting components whose collective behavior can be difficult to predict. Information theory, a branch of mathematics historically associated with questions about encoding and decoding messages, has emerged as something of a <em>lingua franca</em> for those studying complex systems, far exceeding its original narrow domain of communication systems engineering. In the context of complexity science, information theory provides a set of tools which allow researchers to describe a variety of dependencies, including interactions between the component parts of a system, interactions between a system and its environment, and the mereological interaction between the parts and the “whole”.</div><div>In this review aims to provide an accessible introduction to the core of modern information theory, aimed specifically at aspiring (and established) complex systems scientists. This includes standard measures, such as Shannon entropy, relative entropy, and mutual information, before building to more advanced topics, including: information dynamics, measures of statistical complexity, information decomposition, and effective network inference. In addition to detailing the formal definitions, we also make an effort to discuss how information theory can be <em>interpreted</em> and to develop the intuitions behind abstract concepts like “entropy”. The goal is to enable interested readers to understand what information is, and how it is used to better further their own research and education.</div></div>","PeriodicalId":404,"journal":{"name":"Physics Reports","volume":"1148 ","pages":"Pages 1-55"},"PeriodicalIF":29.5,"publicationDate":"2025-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145277961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Universal nonlinear dynamics in damped and driven physical systems: From Pendula via Josephson junctions to power grids","authors":"Subrata Ghosh ,&nbsp;Linuo Xue ,&nbsp;Arindam Mishra ,&nbsp;Suman Saha ,&nbsp;Dawid Dudkowski ,&nbsp;Syamal K. Dana ,&nbsp;Tomasz Kapitaniak ,&nbsp;Jürgen Kurths ,&nbsp;Peng Ji ,&nbsp;Chittaranjan Hens","doi":"10.1016/j.physrep.2025.09.005","DOIUrl":"10.1016/j.physrep.2025.09.005","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Understanding the collective behavior of dynamical systems is essential for explaining various emergent phenomena in natural and engineered settings. A key step in this process is formulating an appropriate mathematical description of the individual systems and network of systems. In this context, a range of physical systems is considered here, including the classical pendula, superconducting Josephson junctions, power grids, and various others. Despite the diversity of the systems in terms of physical structure and their application domains, they exhibit strikingly similar dynamical features, namely, phase dynamics governed by inertia and damping, and in their response to external forcing. This observation creates interest and motivates a search for a unified theoretical framework capable of capturing the fundamentals of their dynamical behaviors exhibited across the systems. This review critically examines the up-to-date research activities on the dynamics of the second-order phase oscillator, henceforth claimed here as a universality class by its own merits as a simple nonlinear dynamical model representing a broad class of physical systems. It offers a common mathematical framework to develop a comprehensive understanding, from a general perspective, that bridges, the theoretical and experimental observations of pendulum motion, Josephson junctions, and power grids and their collective behaviors. While each of these systems has been discussed in disparate physical contexts, their underlying mathematical structures reveal strong commonalities. In particular, we highlight the importance of analyzing these systems through the lens of nonlinear phase dynamics to uncover their shared mechanisms and system-specific variety of behaviors as well. This survey mainly focuses on some specific interrelated themes: (i) collective phenomena and emergent synchronization; (ii) the role of heterogeneity in terms of system parameters and effects of noise on the emergent dynamics; (iii) multi-stability and complex transient regimes; (iv) the integration of machine learning for model discovery, control, and prediction; and (v) the broader applicability of phase oscillator models across diverse domains beyond the canonical systems considered here. By systematically comparing the dynamical behaviors of the varied physical systems within a cohesive mathematical framework of second-order phase oscillators, this review seeks for the universal and distinctive features of nonlinear dynamics of the three systems, their collective behaviors such as emergent synchrony, partial synchrony, or chimera states, and specifically explains real-life phenomena, and crowd synchrony that may lead to a collapse of a footbridge and the failure of a power grid. Besides our main emphasis on these systems, brief notes have been added on other systems where this second-order phase model explains their dynamical properties. A broad synthesis on the topic will not only deepen our ","PeriodicalId":404,"journal":{"name":"Physics Reports","volume":"1147 ","pages":"Pages 1-112"},"PeriodicalIF":29.5,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145218877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantum entanglement in cosmology","authors":"Alessio Belfiglio ,&nbsp;Orlando Luongo ,&nbsp;Stefano Mancini","doi":"10.1016/j.physrep.2025.09.001","DOIUrl":"10.1016/j.physrep.2025.09.001","url":null,"abstract":"<div><div>We discuss recent progress in the study of entanglement within cosmological frameworks, focusing on both momentum and position-space approaches and also reviewing the possibility to directly extract entanglement from quantum fields. Entanglement generation in expanding spacetimes can be traced back to the phenomenon of gravitational particle production, according to which the background gravitational field may transfer energy and momentum to quantum fields. The corresponding entanglement amount and its mode dependence are both sensitive to the field statistics and to the details of spacetime expansion, thus encoding information about the background. Gravitational production processes also play a key role in addressing the quantum-to-classical transition of cosmological perturbations. In order to directly extract entanglement from quantum fields, local interactions with additional quantum systems, working as detectors, have been suggested, leading to the formulation of the entanglement harvesting protocol. Despite harvesting procedures are currently unfeasible from an experimental point of view, various proposals for implementation exist and a proper modeling of detectors and local interactions is crucial to address entanglement extraction via realistic setups. In the final part of the work, we address entanglement characterization in position space, primarily focusing on black hole spacetimes. We first investigate a possible interpretation of Bekenstein–Hawking black hole entropy in terms of the entanglement entropy arising in discrete quantum field theories, on account of the area law. Then, we discuss the resolution of the black hole information paradox via the gravitational fine-grained entropy formula, which provides a new way to compute the entropy of Hawking radiation and allows to preserve unitarity in black hole evaporation processes.</div></div>","PeriodicalId":404,"journal":{"name":"Physics Reports","volume":"1146 ","pages":"Pages 1-47"},"PeriodicalIF":29.5,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145134896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Vegetation dynamics: Modeling, mechanisms, and emergent properties","authors":"Li-Feng Hou ,&nbsp;Li Li ,&nbsp;Renfei Chen ,&nbsp;Yong-Ping Wu ,&nbsp;Guo-Lin Feng ,&nbsp;Gui-Quan Sun","doi":"10.1016/j.physrep.2025.09.003","DOIUrl":"10.1016/j.physrep.2025.09.003","url":null,"abstract":"<div><div>As a core component of terrestrial ecosystems, vegetation plays an irreplaceable role in regulating climate and maintaining ecological balance. However, vegetation dynamics often exhibit strong spatial heterogeneity and nonlinear responses, necessitating the development of an integrated modeling and analysis framework to reveal their underlying mechanisms and guide restoration efforts. This review systematically summarizes recent advances and key methodologies in vegetation dynamics research, focusing on four major dimensions: modeling mechanisms, nonlinear behaviors, ecosystem resilience assessment, and restoration pathway optimization. We first examine reaction–diffusion models based on representative ecological mechanisms such as scale-dependent feedbacks, motility-induced phase separation, and belowground interactions, and introduce stochastic and data-driven models to better capture the uncertainty and multi-source complexity inherent in natural systems. The review also explores nonlinear phenomena such as multistability, regime shifts, and localized structures, employing bifurcation analysis and amplitude equations to investigate pattern selection and system stability. We further review a range of early warning signal indicators based on critical slowing down, spatial patterns, and entropy, and introduce machine learning approaches to enhance predictive capability. Furthermore, we comprehensively review various optimal intervention methods including terminal control, boundary control, and sparse control. Finally, we discuss current challenges and future opportunities in theoretical integration, practical implementation, and cross-scale coordination. This review aims to provide systematic theoretical support and practical guidance for ecological modeling, restoration engineering, and global environmental governance.</div></div>","PeriodicalId":404,"journal":{"name":"Physics Reports","volume":"1145 ","pages":"Pages 1-87"},"PeriodicalIF":29.5,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"High entropy superconductors","authors":"Yahua He ,&nbsp;Kaiyu Ma ,&nbsp;Jing You ,&nbsp;Md. Shahriar A. Hossain ,&nbsp;Muhammad Nadeem ,&nbsp;Xiaolin Wang","doi":"10.1016/j.physrep.2025.09.002","DOIUrl":"10.1016/j.physrep.2025.09.002","url":null,"abstract":"<div><div>High entropy materials have emerged as a focal point of scientific investigation in recent decades due to their exceptional properties, which offer substantial improvements in various domains, including alloy development, catalysis, and condensed matter physics. High entropy superconductors (HESs), in particular, have attracted significant interest due to their entropy-driven superior superconducting properties, making them promise for practical applications. Beyond the advancements seen in cuprates, nickelates, hydrides, iron-based superconductors, and twisted 2D material-based superconductors, HESs demonstrate robust superconductivity under extreme conditions such as high pressure and radiation. These distinctive attributes have established HESs as a unique class within the superconducting landscape, providing a novel platform for discovering new superconductors. This review marks the 10th anniversary of HESs, following their discovery in 2014, and provides a comprehensive overview of HESs, categorizing them into five key systems: high entropy alloys, layered BiS₂ compounds, NaCl-type structures, <em>RE</em>BCO cuprates (<em>RE:</em> rare earth elements), and other variants. It traces the development of HESs and systematically analyzes the impact of high entropy on superconductivity. The review highlights notable features of HESs, such as their exceptional mechanical properties, radiation resistance, and robust superconductivity under high pressure—features that have often been underappreciated. Furthermore, it advocates for expanding research on HESs, emphasizing the importance of developing functional HESs for practical applications.</div></div>","PeriodicalId":404,"journal":{"name":"Physics Reports","volume":"1144 ","pages":"Pages 1-44"},"PeriodicalIF":29.5,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145108469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The anomalous magnetic moment of the muon in the Standard Model: an update","authors":"R. Aliberti ,&nbsp;T. Aoyama ,&nbsp;E. Balzani ,&nbsp;A. Bashir ,&nbsp;G. Benton ,&nbsp;J. Bijnens ,&nbsp;V. Biloshytskyi ,&nbsp;T. Blum ,&nbsp;D. Boito ,&nbsp;M. Bruno ,&nbsp;E. Budassi ,&nbsp;S. Burri ,&nbsp;L. Cappiello ,&nbsp;C.M. Carloni Calame ,&nbsp;M. Cè ,&nbsp;V. Cirigliano ,&nbsp;D.A. Clarke ,&nbsp;G. Colangelo ,&nbsp;L. Cotrozzi ,&nbsp;M. Cottini ,&nbsp;A.S. Zhevlakov","doi":"10.1016/j.physrep.2025.08.002","DOIUrl":"10.1016/j.physrep.2025.08.002","url":null,"abstract":"<div><div>We present the current Standard Model (SM) prediction for the muon anomalous magnetic moment, <span><math><msub><mrow><mi>a</mi></mrow><mrow><mi>μ</mi></mrow></msub></math></span>, updating the first White Paper (WP20) <span><span>[1]</span></span>. The pure QED and electroweak contributions have been further consolidated, while hadronic contributions continue to be responsible for the bulk of the uncertainty of the SM prediction. Significant progress has been achieved in the hadronic light-by-light scattering contribution using both the data-driven dispersive approach as well as lattice-QCD calculations, leading to a reduction of the uncertainty by almost a factor of two. The most important development since WP20 is the change in the estimate of the leading-order hadronic-vacuum-polarization (LO HVP) contribution. A new measurement of the <span><math><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math></span> cross section by CMD-3 has increased the tensions among data-driven dispersive evaluations of the LO HVP contribution to a level that makes it impossible to combine the results in a meaningful way. At the same time, the attainable precision of lattice-QCD calculations has increased substantially and allows for a consolidated lattice-QCD average of the LO HVP contribution with a precision of about 0.9%. Adopting the latter in this update has resulted in a major upward shift of the total SM prediction, which now reads <span><math><mrow><msubsup><mrow><mi>a</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mtext>SM</mtext></mrow></msubsup><mo>=</mo><mn>116</mn><mspace></mspace><mn>592</mn><mspace></mspace><mn>033</mn><mrow><mo>(</mo><mn>62</mn><mo>)</mo></mrow><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>11</mn></mrow></msup></mrow></math></span> (530<!--> <!-->ppb). When compared against the current experimental average based on the E821 experiment and runs 1–6 of E989 at Fermilab, one finds <span><math><mrow><msubsup><mrow><mi>a</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mtext>exp</mtext></mrow></msubsup><mo>−</mo><msubsup><mrow><mi>a</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mtext>SM</mtext></mrow></msubsup><mo>=</mo><mn>38</mn><mrow><mo>(</mo><mn>63</mn><mo>)</mo></mrow><mo>×</mo><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>−</mo><mn>11</mn></mrow></msup></mrow></math></span>, which implies that there is no tension between the SM and experiment at the current level of precision. The final precision of E989 (127 ppb) is the target of future efforts by the Theory Initiative. The resolution of the tensions among data-driven dispersive evaluations of the LO HVP contribution will be a key element in this endeavor.</div></div>","PeriodicalId":404,"journal":{"name":"Physics Reports","volume":"1143 ","pages":"Pages 1-158"},"PeriodicalIF":29.5,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145027658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Corrigendum to “Six decades of the FitzHugh–Nagumo model: A guide through its spatio-temporal dynamics and influence across disciplines” [Phys. Rep. 1096 (2024) 1–39]","authors":"Daniel Cebrián-Lacasa ,&nbsp;Pedro Parra-Rivas ,&nbsp;Daniel Ruiz-Reynés ,&nbsp;Lendert Gelens","doi":"10.1016/j.physrep.2025.08.001","DOIUrl":"10.1016/j.physrep.2025.08.001","url":null,"abstract":"","PeriodicalId":404,"journal":{"name":"Physics Reports","volume":"1140 ","pages":"Pages 47-48"},"PeriodicalIF":29.5,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144895018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The fluctuation–dissipation relations: Growth, diffusion, and beyond","authors":"Márcio Sampaio Gomes-Filho ,&nbsp;Luciano Calheiros Lapas ,&nbsp;Ewa Gudowska-Nowak ,&nbsp;Fernando Albuquerque Oliveira","doi":"10.1016/j.physrep.2025.07.004","DOIUrl":"10.1016/j.physrep.2025.07.004","url":null,"abstract":"<div><div>In this review, we scrutinize historical and modern results on the linear response of dynamical systems to external perturbations with a particular emphasis on the celebrated relationship between fluctuations and dissipation expressed by the fluctuation–dissipation theorem (FDT). The conceptual foundation of FDT originates from the definition of the equilibrium state and Onsager’s regression hypothesis. Over time, the fluctuation–dissipation relation has been vividly investigated also in systems far from equilibrium, which often exhibit wild fluctuations in measured parameters. In this review, we recall the major formulations of the FDT, including those proposed by Langevin, Onsager and Kubo. We discuss the role of fluctuations in a broad class of growth and diffusion phenomena and examine the violation of the FDT resulting from a transition from Euclidean to fractal geometry. Finally, we highlight possible generalizations of the FDT formalism and discuss situations where the relation breaks down and is no longer applicable.</div></div>","PeriodicalId":404,"journal":{"name":"Physics Reports","volume":"1141 ","pages":"Pages 1-43"},"PeriodicalIF":29.5,"publicationDate":"2025-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144770851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optically assisted ultrafast spintronics: A review","authors":"Surya Narain Dikshit ,&nbsp;Arshid Nisar ,&nbsp;Brahmdutta Dixit ,&nbsp;Baljinder Kaur ,&nbsp;Alok Kumar Shukla ,&nbsp;Ashutosh Kumar ,&nbsp;Junyang Chen ,&nbsp;Jian-Ping Wang ,&nbsp;Himanshu Fulara ,&nbsp;Brajesh Kumar Kaushik","doi":"10.1016/j.physrep.2025.07.002","DOIUrl":"10.1016/j.physrep.2025.07.002","url":null,"abstract":"<div><div>All-optical switching (AOS) has emerged as a promising technique, utilizing ultrafast lasers with femto or picosecond-pulse durations for modulating magnetization without the use of magnetic fields. This article reviews the state-of-the-art in AOS, focusing on achieving sub-picosecond magnetization reversal in a diverse range of materials, including ferri-magnetic alloys, synthetic ferri-magnets, ferromagnetic multilayers, Heusler alloys, and 2D materials. These materials exhibit remarkable potential for the development of optically driven spintronics devices, offering ultrafast and energy-efficient solutions for circuits and systems, and promising avenues for future photonic integrated circuits. This article also delves into recent advances in opto-spintronic devices, examining their utilization in energy-efficient memory, logic circuits, neuromorphic computing, and terahertz applications. Despite the promising prospects, the integration of opto-spintronic systems into mainstream microelectronic platforms faces several challenges. This review comprehensively discusses these challenges at both the device and system levels, offering insights into potential solutions and future perspectives. By consolidating recent developments and identifying ongoing challenges, this review aims to contribute to the understanding and advancement of AOS in the context of opto-spintronics, paving the way for the next generation of ultrafast and energy-efficient spintronic devices.</div></div>","PeriodicalId":404,"journal":{"name":"Physics Reports","volume":"1140 ","pages":"Pages 1-46"},"PeriodicalIF":23.9,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144653832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Subharmonic modulational instabilities","authors":"Wen-Rong Sun ,&nbsp;Boris A. Malomed","doi":"10.1016/j.physrep.2025.07.001","DOIUrl":"10.1016/j.physrep.2025.07.001","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Benjamin and Feir in 1967 demonstrated that Stokes waves in deep water are unstable against longitudinal sideband perturbations, and this instability leads to the transformation of an initial periodic wave train into a chain of wave packets. Nowadays, this phenomenon is known as the Benjamin–Feir or modulational instability (MI), with a more general definition. In particular, it may be the &lt;em&gt;subharmonic instability&lt;/em&gt;, when periodic wave trains are unstable against perturbations whose spatial period is a multiple of the underlying wave-train’s period. MI is well known as a ubiquitous effect occurring in diverse fields, such as water waves, plasmas, optics and photonics, and Bose–Einstein condensates (BECs). One can examine the initial (i.e., linear) stage of the MI development by the linearization of the governing equations for small perturbations around the initial (unperturbed) periodic wave train. The linearization ceases to be valid when the growing amplitude of the perturbations becomes comparable to the amplitude of the unperturbed periodic wave trains, which makes investigation of the nonlinear stage of the MI-driven dynamics necessary. It is well known that the nonlinear evolution of MI leads to the formation of localized structures, such as solitons, breathers and rogue waves (RWs). Another essential type of the instability is the high-frequency MI (HFMI), which also originates from the water-wave theory and has been extended to other fields of physics. Similar to the classical MI (alias the low-frequency MI (LFMI)), HFMI may also be viewed as a subharmonic instability of periodic wave trains, but with a very small growth rate and narrow intervals of the Floquet exponents in which HFMI occurs. In this review, we mainly focus on the linear and nonlinear dynamics of periodic wave trains in integrable and nearly integrable systems, including the linear and nonlinear stage of the MI development and investigation of the subharmonic MI. &lt;strong&gt;First&lt;/strong&gt;, we review findings concerning HFMI in fluid dynamics. Subsequently, we address outcomes of HFMI in various physical fields produced by the universal nonlinear Schrödinger (NLS) equation, complemented by a spatially periodic potential. &lt;strong&gt;Second&lt;/strong&gt;, we review discoveries regarding MI of cnoidal waves in nearly integrable and non-integrable systems, drawing insights from the consideration of the long-wave-short-wave resonance equation and universal &lt;span&gt;&lt;math&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;ϕ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;/math&gt;&lt;/span&gt; equation. In addition to that, we summarize analytical results pertaining to MI and modulational stability of cnoidal waves in some integrable systems. &lt;strong&gt;Third&lt;/strong&gt;, we review results for the nonlinear stage of the MI development, by introducing exact correspondence between MI and the formation of localized waves, including RWs with ultra-high peak amplitudes in the baseband-MI regime, and the formation of RWs in the zero-wave","PeriodicalId":404,"journal":{"name":"Physics Reports","volume":"1139 ","pages":"Pages 1-62"},"PeriodicalIF":23.9,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}