Journal of Statistical Mechanics: Theory and Experiment - IOPscience

Journal of Statistical Mechanics: Theory and Experiment - IOPscience
Journal of Statistical Mechanics: Theory and Experiment
The International School for Advanced Studies (SISSA)
was founded in 1978 and was the first institution in Italy to promote post-graduate courses leading to a Doctor Philosophiae (or PhD) degree. A centre of excellence among Italian and international universities, the school has around 65 teachers, 100 post docs and 245 PhD students, and is located in Trieste, in a campus of more than 10 hectares with wonderful views over the Gulf of Trieste.
SISSA hosts a very high-ranking, large and multidisciplinary scientific research output. The scientific papers produced by its researchers are published in high impact factor, well-known international journals, and in many cases in the world's most prestigious scientific journals such as Nature and Science. Over 900 students have so far started their careers in the field of mathematics, physics and neuroscience research at SISSA.
SUPPORTS OPEN ACCESS
Journal of Statistical Mechanics: Theory and Experiment
(JSTAT) is a multi-disciplinary, peer-reviewed international journal created by the
International School for Advanced Studies
(SISSA) and
IOP Publishing
(IOP).  JSTAT covers all aspects of statistical physics, including experimental work that impacts on the subject.
Submit
an article
opens in new tab
RSS
Sign up for new issue notifications
Impact factor
1.9
Citescore
4.5
Deep double descent: where bigger models and more data hurt
Preetum Nakkiran
et al
J. Stat. Mech.
(2021) 124003
View article
, Deep double descent: where bigger models and more data hurt
PDF
, Deep double descent: where bigger models and more data hurt
We show that a variety of modern deep learning tasks exhibit a ‘double-descent’ phenomenon where, as we increase model size, performance first gets
worse
and then gets better. Moreover, we show that double descent occurs not just as a function of model size, but also as a function of the number of training epochs. We unify the above phenomena by defining a new complexity measure we call the
effective model complexity
and conjecture a generalized double descent with respect to this measure. Furthermore, our notion of model complexity allows us to identify certain regimes where increasing (even quadrupling) the number of train samples actually
hurts
test performance.
Fast unfolding of communities in large networks
Vincent D Blondel
et al
J. Stat. Mech.
(2008) P10008
View article
, Fast unfolding of communities in large networks
PDF
, Fast unfolding of communities in large networks
We propose a simple method to extract the community structure of large networks. Our
method is a heuristic method that is based on modularity optimization. It is shown to
outperform all other known community detection methods in terms of computation time.
Moreover, the quality of the communities detected is very good, as measured by the
so-called modularity. This is shown first by identifying language communities in a Belgian
mobile phone network of 2 million customers and by analysing a web graph of 118 million
nodes and more than one billion links. The accuracy of our algorithm is also verified on ad
hoc modular networks.
The following article is
Open access
Introduction to latent variable energy-based models: a path toward autonomous machine intelligence
Anna Dawid and Yann LeCun
J. Stat. Mech.
(2024) 104011
View article
, Introduction to latent variable energy-based models: a path toward autonomous machine intelligence
PDF
, Introduction to latent variable energy-based models: a path toward autonomous machine intelligence
Current automated systems have crucial limitations that need to be addressed before artificial intelligence can reach human-like levels and bring new technological revolutions. Among others, our societies still lack level-5 self-driving cars, domestic robots, and virtual assistants that learn reliable world models, reason, and plan complex action sequences. In these notes, we summarize the main ideas behind the architecture of autonomous intelligence of the future proposed by Yann LeCun. In particular, we introduce energy-based and latent variable models and combine their advantages in the building block of LeCun’s proposal, that is, in the hierarchical joint-embedding predictive architecture.
The following article is
Open access
Coarse-graining nonequilibrium diffusions with Markov chains
Ramón Nartallo-Kaluarachchi
et al
J. Stat. Mech.
(2026) 033205
View article
, Coarse-graining nonequilibrium diffusions with Markov chains
PDF
, Coarse-graining nonequilibrium diffusions with Markov chains
We investigate nonequilibrium steady-state dynamics in both continuous- and discrete-state stochastic processes. Our analysis focuses on planar diffusion dynamics and their coarse-grained approximations by discrete-state Markov chains. Using finite-volume approximations, we derive an approximate master equation directly from the underlying diffusion and show that this discretisation preserves key features of the nonequilibrium steady-state. In particular, we show that the entropy production rate (EPR) of the approximation converges as the number of discrete states goes to the limit. These results are illustrated with analytically solvable diffusions and numerical experiments on nonlinear processes, demonstrating how this approach can be used to explore the dependence of EPR on model parameters. Finally, we address the problem of inferring discrete-state Markov models from continuous stochastic trajectories. We show that discrete-state models significantly underestimate the true EPR. However, we also show that they can provide tests to determine if a stationary planar diffusion is out of equilibrium. This property is illustrated with both simulated data and empirical trajectories from schooling fish.
The following article is
Open access
The quantum Mpemba effect in closed systems: from theory to experiment
Pasquale Calabrese
J. Stat. Mech.
(2026) 034002
View article
, The quantum Mpemba effect in closed systems: from theory to experiment
PDF
, The quantum Mpemba effect in closed systems: from theory to experiment
The Mpemba effect refers to a counterintuitive phenomenon whereby a system initially prepared further from equilibrium may relax faster than one prepared closer to equilibrium. While extensively studied in classical nonequilibrium physics, its extension to isolated quantum systems only started in the last few years. In this contribution we review recent progress on the quantum Mpemba effect in closed many-body systems, emphasizing the role of reduced density matrix, entanglement and symmetry restoration. We discuss why and how the entanglement asymmetry provides a natural and experimentally accessible framework to characterize Mpemba-like behavior in unitary quantum evolution.
The following article is
Open access
Fast unfolding of communities in large networks: 15 years later
Vincent Blondel
et al
J. Stat. Mech.
(2024) 10R001
View article
, Fast unfolding of communities in large networks: 15 years later
PDF
, Fast unfolding of communities in large networks: 15 years later
The Louvain method was proposed 15 years ago as a heuristic method for the fast detection of communities in large networks. During this period, it has emerged as one of the most popular methods for community detection: the task of partitioning vertices of a network into dense groups, usually called communities or clusters. Here, after a short introduction to the method, we give an overview of the different generalizations, modifications and improvements that have been proposed in the literature, and also survey the quality functions, beyond modularity, for which it has been implemented. Finally, we conclude with a discussion on the limitations of the method and perspectives for future research.
The following article is
Open access
Pedestrian flow analysis in high-density crowds: continuity equation with Voronoi-based fields
Juliane Adrian
et al
J. Stat. Mech.
(2026) 043401
View article
, Pedestrian flow analysis in high-density crowds: continuity equation with Voronoi-based fields
PDF
, Pedestrian flow analysis in high-density crowds: continuity equation with Voronoi-based fields
Since the beginning of the century, it has been possible to precisely capture trajectories of pedestrian streams from video recordings. To enable measurements at high density, the heads of pedestrians are marked and tracked, thereby providing a complete representation of the phase space. However, the classical definitions of flow, density, and velocity of pedestrian streams are based on different segments in phase space. In addition, traditional methods fail with high densities of people, as heads move even when a crowd is blocked and standing still. In this study, Voronoi decomposition was used to construct density and velocity fields from pedestrian trajectories to solve this problem. Combined with the continuity equation, a flow equation based on trajectories was derived, exactly satisfying the conservation of particle numbers. The proposed method allows all quantities to be defined within the same segment of phase space, even at scales smaller than the dimensions of a pedestrian. It is shown that these new definitions of flow, density, and velocity are consistent with classical measurements and enable the determination of standstill in pedestrian flows, even when individual body parts are moving. These properties allow inconsistencies in the state of the art of pedestrian fundamental diagrams to be scrutinised.
The following article is
Open access
Classification of diffusion processes in dimension
via the Carleman approach with applications to models involving additive, multiplicative, or square-root noises
Cécile Monthus
J. Stat. Mech.
(2026) 033204
View article
, Classification of diffusion processes in dimension d via the Carleman approach with applications to models involving additive, multiplicative, or square-root noises
PDF
, Classification of diffusion processes in dimension d via the Carleman approach with applications to models involving additive, multiplicative, or square-root noises
The Carleman approach is a popular method in the field of deterministic classical dynamics for replacing a finite number
of nonlinear differential equations by an infinite-dimensional linear system. Here, this approach is applied to a system of
stochastic differential equations for
when the forces and the diffusion-matrix elements are polynomials, to write the linear system governing the dynamics of the averaged values
labeled by the
integers
. The natural decomposition of the Carleman matrix into blocks associated with the global degree
is useful to identify the models with the simplest spectral decompositions in the bi-orthogonal basis of right and left eigenvectors. This analysis is then applied to models with a single noise per coordinate, which can be either additive or multiplicative or square root or with two types of noise per coordinate, with many examples in dimensions
. In
= 1, the Carleman matrix governing the dynamics of the moments
is diagonal for the geometric Brownian motion, whereas it is lower triangular for the family of Pearson diffusions containing the Ornstein–Uhlenbeck and the Square–Root processes, as well as the Kesten, the Fisher–Snedecor, and the Student processes that converge toward steady states with power-law tails. In dimension
= 2, the Carleman matrix governing the dynamics of the correlations
has a natural decomposition into blocks associated to the global degree
, and we discuss the simplest models where the Carleman matrix is either block-diagonal, block-lower-triangular, or block-upper-triangular.
The following article is
Open access
Boltzmann to Lindblad: classical and quantum approaches to out-of-equilibrium statistical mechanics
Stefano Giordano
et al
J. Stat. Mech.
(2026) 033101
View article
, Boltzmann to Lindblad: classical and quantum approaches to out-of-equilibrium statistical mechanics
PDF
, Boltzmann to Lindblad: classical and quantum approaches to out-of-equilibrium statistical mechanics
Open quantum systems play a central role in current nanoscale technologies, such as molecular electronics, quantum heat engines, quantum computation and information processing. A major theoretical challenge is to construct dynamical models that are simultaneously consistent with classical thermodynamics and with the requirement of complete positivity of quantum evolution. In this work we develop a framework that addresses this issue by systematically extending classical stochastic dynamics to the quantum domain. We begin by formulating a generalized Langevin equation in which both friction and noise act symmetrically on the two Hamiltonian equations. From this, we derive a generalized Klein–Kramers equation expressed in terms of Poisson brackets, and we show that it admits the Boltzmann distribution as its stationary solution while fulfilling the first and second laws of thermodynamics along individual trajectories. Applying canonical quantization to this classical framework yields two distinct quantum master equations, depending on whether the friction operators are taken to be Hermitian or non-Hermitian. By analyzing the dynamics of a harmonic oscillator, we determine the conditions under which these equations reduce to a Lindblad-type generator. Our results demonstrate that complete positivity is ensured only when friction and noise are included in both Hamiltonian equations, fully justifying the classical construction. Moreover, we find that the friction coefficients must adhere to the same positivity condition in both the Hermitian and non-Hermitian formulations, revealing a form of universality that transcends the specific operator representation. The formalism developed here presents a thermodynamically consistent and completely positive quantum extension of classical stochastic mechanics. It offers a versatile tool for deriving quantum versions of thermodynamic laws and is directly applicable to a broad class of non-equilibrium nanoscale systems of current theoretical and technological interest.
The following article is
Open access
Thermal Casimir effect in the spin–orbit coupled Bose gas
Marek Napiórkowski and Pawel Jakubczyk
J. Stat. Mech.
(2026) 033102
View article
, Thermal Casimir effect in the spin–orbit coupled Bose gas
PDF
, Thermal Casimir effect in the spin–orbit coupled Bose gas
We study the thermal Casimir effect in ideal Bose gases with spin–orbit (S–O) coupling of Rashba type below the critical temperature for Bose–Einstein condensation. In contrast to the standard situation involving no S–O coupling, the system exhibits long-ranged Casimir forces in both two and three dimensions (
= 2 and
= 3). We identify the relevant scaling variable involving the ratio
of the separation between the confining walls
and the S–O coupling magnitude
. We derive and discuss the corresponding scaling functions for the Casimir energy. In all the considered cases, the resulting Casimir force is attractive and the S–O coupling
has impact on its magnitude. In
= 3 the exponent governing the decay of the Casimir force becomes modified by the presence of the S–O coupling, and its value depends on the orientation of the confining walls relative to the plane defined by the Rashba coupling. In
= 2 the obtained Casimir force displays a singular behavior in the limit of vanishing
The following article is
Open access
Mode-coupling theory of the glass transition for Brownian particles in a periodic potential
Robert Schlothauer
et al
J. Stat. Mech.
(2026) 043204
View article
, Mode-coupling theory of the glass transition for Brownian particles in a periodic potential
PDF
, Mode-coupling theory of the glass transition for Brownian particles in a periodic potential
We adapt the mode-coupling theory of the glass transition, originally developed for modulated liquids with Newtonian dynamics, to colloidal liquids. The modulation reduces continuous translational invariance to a discrete lattice symmetry, which we encode by resolving density fluctuations into Brillouin-zone wave vectors and reciprocal-lattice indices. Using the Mori–Zwanzig projection-operator formalism, we derive exact equations of motion for generalized intermediate scattering functions. For Brownian dynamics, the memory kernel naturally decomposes into an irreducible part that reflects anisotropic transport parallel and perpendicular to the modulation. Within the mode-coupling closure, these irreducible kernels assume the same bilinear form as in the Newtonian theory. Consequently, the slow structural relaxation near the glass transition, including scaling laws and critical exponents, is universal and independent of microscopic dynamics. Differences between Brownian and Newtonian cases are confined to short-time propagators. This framework unifies glassy dynamics in modulated colloidal and atomic systems and facilitates quantitative comparison with experiments and simulations.
The following article is
Open access
Strain-rate, temperature and size effects on the mechanical behavior of fiber bundles
Jérôme Weiss
J. Stat. Mech.
(2026) 043303
View article
, Strain-rate, temperature and size effects on the mechanical behavior of fiber bundles
PDF
, Strain-rate, temperature and size effects on the mechanical behavior of fiber bundles
The mechanical characteristics of fibers (of various materials), as well as of fiber bundles, are of primary importance for the design and the mechanical behavior of textiles, or of fibrous and composite materials. These characteristics are classically determined from strain-rate-controlled tensile testing, generally assuming a negligible role of thermal activation on damage and fracturing processes. Under this assumption, the distribution of individual fiber strengths can be deduced from a downscaling of the macroscopic mechanical behavior at the bundle scale. There is, however, considerable experimental evidence of strain-rate and temperature effects on the mechanical behavior of individual fibers or bundles, which can also creep under constant applied load. This indicates a strong role of thermal activation on these processes. Here, these effects are analyzed from a fiber-bundle model with equal load sharing, in which thermal activation of fiber breakings is introduced from a kinetic Monte Carlo algorithm adapted for time-varying stresses. This allows one to rationalize these rate or temperature effects, such as a decrease in bundle strength, strain at peak stress, and apparent Young’s modulus with decreasing strain rate and/or increasing temperature. This also shows that the classical downscaling procedure used to estimate the distribution of individual fiber strengths from the mechanical behavior at the bundle scale should be considered with caution. If mechanical testing of the bundle is performed under conditions favoring the role of thermal activation (e.g. low applied strain rate), this procedure can strongly underestimate the intrinsic (athermal) Weibull’s parameters of the fiber strength’s distribution. The same model is also used to explore size (number of fibers) effects on bundle mechanical response.
The following article is
Open access
Generalization performance of narrow shallow neural networks in the teacher–student setting
Rodrigo Pérez Ortiz
et al
J. Stat. Mech.
(2026) 043405
View article
, Generalization performance of narrow shallow neural networks in the teacher–student setting
PDF
, Generalization performance of narrow shallow neural networks in the teacher–student setting
Understanding the generalization properties of neural networks on simple input–output distributions is key to explaining their performance on real datasets. The classical teacher–student setting, where a network is trained on data generated by a teacher model, provides a canonical theoretical test bed. In this context, a complete theoretical characterization of fully connected one-hidden-layer networks with generic activation functions remains missing. In this work, we develop a general framework for such networks with large width, yet much smaller than the input dimension. Using methods from statistical physics, we derive closed-form expressions for the typical performance of both finite-temperature (Bayesian) and empirical risk minimization estimators in terms of a small number of order parameters. We uncover a transition to a specialization phase, where hidden neurons align with teacher features once the number of samples becomes sufficiently large and proportional to the number of network parameters. Our theory accurately predicts the generalization error of networks trained on regression and classification tasks using either noisy full-batch gradient descent (GD) (Langevin dynamics) or deterministic full-batch GD.
Semi-Markovian dynamics of a self-propelled particle in a confined environment: a large-deviation study
Shabnam Sohrabi and Farhad H Jafarpour
J. Stat. Mech.
(2026) 043203
View article
, Semi-Markovian dynamics of a self-propelled particle in a confined environment: a large-deviation study
PDF
, Semi-Markovian dynamics of a self-propelled particle in a confined environment: a large-deviation study
We study the large deviations of the time-integrated current for a self-propelled particle moving within a confined environment. The dynamics is modeled as a semi-Markovian process, where the transitions between a
normal running phase
(Phase 0) and a
wall-attached phase
(Phase 1) are governed by time-dependent reset probabilities. We study two different examples: In the first case, the particle undergoes a biased random walk in Phase 0, while it intermittently resets and interacts with the container boundaries, remaining stationary in Phase 1. In this scenario, the reset probabilities for transitions between the two phases follow an ‘aging’ logic. In the second case, the particle alternates between two active phases: a Markovian Phase 0 characterized by memoryless, downstream-biased motion, and a semi-Markovian Phase 1 with a reversed, upstream bias representing boundary-attached navigation. Here, we assume a time-independent survival probability in Phase 0 and a time-dependent one in Phase 1. By analyzing the scaled cumulant generating function in the long-time limit, we derive the conditions for dynamical phase transition (DPT)s in the fluctuations of the particle velocity. We demonstrate that, depending on the aging strength, the system exhibits either discontinuous (first-order) or continuous (second-order) DPTs. Analytical predictions are validated via computer simulations.
The following article is
Open access
Pedestrian flow analysis in high-density crowds: continuity equation with Voronoi-based fields
Juliane Adrian
et al
J. Stat. Mech.
(2026) 043401
View article
, Pedestrian flow analysis in high-density crowds: continuity equation with Voronoi-based fields
PDF
, Pedestrian flow analysis in high-density crowds: continuity equation with Voronoi-based fields
Since the beginning of the century, it has been possible to precisely capture trajectories of pedestrian streams from video recordings. To enable measurements at high density, the heads of pedestrians are marked and tracked, thereby providing a complete representation of the phase space. However, the classical definitions of flow, density, and velocity of pedestrian streams are based on different segments in phase space. In addition, traditional methods fail with high densities of people, as heads move even when a crowd is blocked and standing still. In this study, Voronoi decomposition was used to construct density and velocity fields from pedestrian trajectories to solve this problem. Combined with the continuity equation, a flow equation based on trajectories was derived, exactly satisfying the conservation of particle numbers. The proposed method allows all quantities to be defined within the same segment of phase space, even at scales smaller than the dimensions of a pedestrian. It is shown that these new definitions of flow, density, and velocity are consistent with classical measurements and enable the determination of standstill in pedestrian flows, even when individual body parts are moving. These properties allow inconsistencies in the state of the art of pedestrian fundamental diagrams to be scrutinised.
Field-theory approach to flat polymerized membranes
Simon Metayer and Sofian Teber
J. Stat. Mech.
(2025) 092001
View article
, Field-theory approach to flat polymerized membranes
PDF
, Field-theory approach to flat polymerized membranes
We review the field-theoretic renormalization-group (RG) approach toward the critical properties of flat polymerized membranes. We start with a presentation of a flexural effective model that is entirely expressed in terms of a transverse (flexural) field with nonlocal interactions. We then provide a detailed account of the full three-loop computations of the RG functions of this model within the dimensional regularization scheme. The latter allows us to consider the general case of a
-dimensional membrane embedded in a
-dimensional space. Focusing on the critical flat phase of two-dimensional membranes (
= 2) in three-dimensional space (
= 3), we analyze the corresponding flow diagram and present the derivation of the anomalous stiffness. The latter controls all the other critical exponents of the theory, such as the roughness exponent and the scaling of the elastic constants. State-of-the-art four-loop results, discussions on the structure of the perturbative series, and comparisons with other approaches are also provided.
The following article is
Open access
Fast unfolding of communities in large networks: 15 years later
Vincent Blondel
et al
J. Stat. Mech.
(2024) 10R001
View article
, Fast unfolding of communities in large networks: 15 years later
PDF
, Fast unfolding of communities in large networks: 15 years later
The Louvain method was proposed 15 years ago as a heuristic method for the fast detection of communities in large networks. During this period, it has emerged as one of the most popular methods for community detection: the task of partitioning vertices of a network into dense groups, usually called communities or clusters. Here, after a short introduction to the method, we give an overview of the different generalizations, modifications and improvements that have been proposed in the literature, and also survey the quality functions, beyond modularity, for which it has been implemented. Finally, we conclude with a discussion on the limitations of the method and perspectives for future research.
The following article is
Open access
Network meta-analysis: a statistical physics perspective
Annabel L Davies and Tobias Galla
J. Stat. Mech.
(2022) 11R001
View article
, Network meta-analysis: a statistical physics perspective
PDF
, Network meta-analysis: a statistical physics perspective
Network meta-analysis (NMA) is a technique used in medical statistics to combine evidence from multiple medical trials. NMA defines an inference and information processing problem on a network of treatment options and trials connecting the treatments. We believe that statistical physics can offer useful ideas and tools for this area, including from the theory of complex networks, stochastic modelling and simulation techniques. The lack of a unique source that would allow physicists to learn about NMA effectively is a barrier to this. In this article we aim to present the ‘NMA problem’ and existing approaches to it coherently and in a language accessible to statistical physicists. We also summarise existing points of contact between statistical physics and NMA, and describe our ideas of how physics might make a difference for NMA in the future. The overall goal of the article is to attract physicists to this interesting, timely and worthwhile field of research.
Kuramoto model of synchronization: equilibrium and nonequilibrium aspects
Shamik Gupta
et al
J. Stat. Mech.
(2014) R08001
View article
, Kuramoto model of synchronization: equilibrium and nonequilibrium aspects
PDF
, Kuramoto model of synchronization: equilibrium and nonequilibrium aspects
The phenomenon of spontaneous synchronization, particularly within the framework of the Kuramoto model, has been a subject of intense research over the years. The model comprises oscillators with distributed natural frequencies interacting through a mean-field coupling, and serves as a paradigm to study synchronization. In this review, we put forward a general framework in which we discuss in a unified way known results with more recent developments obtained for a generalized Kuramoto model that includes inertial effects and noise. We describe the model from a different perspective, highlighting the long-range nature of the interaction between the oscillators, and emphasizing the equilibrium and out-of-equilibrium aspects of its dynamics from a statistical physics point of view. In this review, we first introduce the model and discuss both for the noiseless and noisy dynamics and for unimodal frequency distributions the synchronization transition that occurs in the stationary state. We then introduce the generalized model, and analyze its dynamics using tools from statistical mechanics. In particular, we discuss its synchronization phase diagram for unimodal frequency distributions. Next, we describe deviations from the mean-field setting of the Kuramoto model. To this end, we consider the generalized Kuramoto dynamics on a one-dimensional periodic lattice on the sites of which the oscillators reside and interact with one another with a coupling that decays as an inverse power-law of their separation along the lattice. For two specific cases, namely, in the absence of noise and inertia, and in the case when the natural frequencies are the same for all the oscillators, we discuss how the long-time transition to synchrony is governed by the dynamics of the mean-field mode (zero Fourier mode) of the spatial distribution of the oscillator phases.
The following article is
Open access
Mode-coupling theory of the glass transition for Brownian particles in a periodic potential
Robert Schlothauer
et al
J. Stat. Mech.
(2026) 043204
View article
, Mode-coupling theory of the glass transition for Brownian particles in a periodic potential
PDF
, Mode-coupling theory of the glass transition for Brownian particles in a periodic potential
We adapt the mode-coupling theory of the glass transition, originally developed for modulated liquids with Newtonian dynamics, to colloidal liquids. The modulation reduces continuous translational invariance to a discrete lattice symmetry, which we encode by resolving density fluctuations into Brillouin-zone wave vectors and reciprocal-lattice indices. Using the Mori–Zwanzig projection-operator formalism, we derive exact equations of motion for generalized intermediate scattering functions. For Brownian dynamics, the memory kernel naturally decomposes into an irreducible part that reflects anisotropic transport parallel and perpendicular to the modulation. Within the mode-coupling closure, these irreducible kernels assume the same bilinear form as in the Newtonian theory. Consequently, the slow structural relaxation near the glass transition, including scaling laws and critical exponents, is universal and independent of microscopic dynamics. Differences between Brownian and Newtonian cases are confined to short-time propagators. This framework unifies glassy dynamics in modulated colloidal and atomic systems and facilitates quantitative comparison with experiments and simulations.
The following article is
Open access
Strain-rate, temperature and size effects on the mechanical behavior of fiber bundles
Jérôme Weiss
J. Stat. Mech.
(2026) 043303
View article
, Strain-rate, temperature and size effects on the mechanical behavior of fiber bundles
PDF
, Strain-rate, temperature and size effects on the mechanical behavior of fiber bundles
The mechanical characteristics of fibers (of various materials), as well as of fiber bundles, are of primary importance for the design and the mechanical behavior of textiles, or of fibrous and composite materials. These characteristics are classically determined from strain-rate-controlled tensile testing, generally assuming a negligible role of thermal activation on damage and fracturing processes. Under this assumption, the distribution of individual fiber strengths can be deduced from a downscaling of the macroscopic mechanical behavior at the bundle scale. There is, however, considerable experimental evidence of strain-rate and temperature effects on the mechanical behavior of individual fibers or bundles, which can also creep under constant applied load. This indicates a strong role of thermal activation on these processes. Here, these effects are analyzed from a fiber-bundle model with equal load sharing, in which thermal activation of fiber breakings is introduced from a kinetic Monte Carlo algorithm adapted for time-varying stresses. This allows one to rationalize these rate or temperature effects, such as a decrease in bundle strength, strain at peak stress, and apparent Young’s modulus with decreasing strain rate and/or increasing temperature. This also shows that the classical downscaling procedure used to estimate the distribution of individual fiber strengths from the mechanical behavior at the bundle scale should be considered with caution. If mechanical testing of the bundle is performed under conditions favoring the role of thermal activation (e.g. low applied strain rate), this procedure can strongly underestimate the intrinsic (athermal) Weibull’s parameters of the fiber strength’s distribution. The same model is also used to explore size (number of fibers) effects on bundle mechanical response.
The following article is
Open access
Generalization performance of narrow shallow neural networks in the teacher–student setting
Rodrigo Pérez Ortiz
et al
J. Stat. Mech.
(2026) 043405
View article
, Generalization performance of narrow shallow neural networks in the teacher–student setting
PDF
, Generalization performance of narrow shallow neural networks in the teacher–student setting
Understanding the generalization properties of neural networks on simple input–output distributions is key to explaining their performance on real datasets. The classical teacher–student setting, where a network is trained on data generated by a teacher model, provides a canonical theoretical test bed. In this context, a complete theoretical characterization of fully connected one-hidden-layer networks with generic activation functions remains missing. In this work, we develop a general framework for such networks with large width, yet much smaller than the input dimension. Using methods from statistical physics, we derive closed-form expressions for the typical performance of both finite-temperature (Bayesian) and empirical risk minimization estimators in terms of a small number of order parameters. We uncover a transition to a specialization phase, where hidden neurons align with teacher features once the number of samples becomes sufficiently large and proportional to the number of network parameters. Our theory accurately predicts the generalization error of networks trained on regression and classification tasks using either noisy full-batch gradient descent (GD) (Langevin dynamics) or deterministic full-batch GD.
The following article is
Open access
Pedestrian flow analysis in high-density crowds: continuity equation with Voronoi-based fields
Juliane Adrian
et al
J. Stat. Mech.
(2026) 043401
View article
, Pedestrian flow analysis in high-density crowds: continuity equation with Voronoi-based fields
PDF
, Pedestrian flow analysis in high-density crowds: continuity equation with Voronoi-based fields
Since the beginning of the century, it has been possible to precisely capture trajectories of pedestrian streams from video recordings. To enable measurements at high density, the heads of pedestrians are marked and tracked, thereby providing a complete representation of the phase space. However, the classical definitions of flow, density, and velocity of pedestrian streams are based on different segments in phase space. In addition, traditional methods fail with high densities of people, as heads move even when a crowd is blocked and standing still. In this study, Voronoi decomposition was used to construct density and velocity fields from pedestrian trajectories to solve this problem. Combined with the continuity equation, a flow equation based on trajectories was derived, exactly satisfying the conservation of particle numbers. The proposed method allows all quantities to be defined within the same segment of phase space, even at scales smaller than the dimensions of a pedestrian. It is shown that these new definitions of flow, density, and velocity are consistent with classical measurements and enable the determination of standstill in pedestrian flows, even when individual body parts are moving. These properties allow inconsistencies in the state of the art of pedestrian fundamental diagrams to be scrutinised.
The following article is
Open access
Functional renormalisation for signal detection: dimensional analysis and dimensional phase transition for nearly continuous spectra effective field theory
Riccardo Finotello
et al
J. Stat. Mech.
(2026) 043403
View article
, Functional renormalisation for signal detection: dimensional analysis and dimensional phase transition for nearly continuous spectra effective field theory
PDF
, Functional renormalisation for signal detection: dimensional analysis and dimensional phase transition for nearly continuous spectra effective field theory
Signal detection in high-dimensional data is a critical challenge in data science. While standard methods based on random matrix theory provide sharp detection thresholds for finite-rank perturbations, such as the known Baik–Ben Arous–Péché (BBP) transition, they are often insufficient for realistic data exhibiting nearly continuous (extensive-rank) signal distributions that merge with the noise bulk. In this regime, typically associated with real-world scenarios such as images for computer vision tasks, the signal does not manifest as a clear outlier but as a deformation of the spectral density’s geometry. We use the functional renormalisation group (FRG) framework to probe these subtle spectral deformations. Treating the empirical spectrum as an effective field theory, we define a scale-dependent ‘canonical dimension’ that acts as a sensitive order parameter for the spectral geometry. We show that this dimension undergoes a sharp crossover, interpreted as a ‘dimensional phase transition’, at signal-to-noise ratios significantly lower than the standard BBP threshold. This dimensional instability is shown to correlate with a spontaneous symmetry breaking in the effective potential and a deviation of eigenvector statistics from the universal Porter-Thomas distribution, confirming the consistency of the method. Such behaviour aligns with recent theoretical results on the ‘extensive spike model’, where signal information persists inside the noise bulk before any spectral gap opens. We validate our approach on realistic image datasets, demonstrating that the FRG flow consistently detects the onset of this bulk deformation. Finally, we explore a formalisation of this methodology for analysing nearly continuous spectra, proposing a heuristic criterion for signal detection and a method to estimate the number of independent noise components based on the cyclic stability of these canonical dimensions.
The following article is
Open access
On the nature of the spin glass transition
Gesualdo Delfino
J. Stat. Mech.
(2026) 043201
View article
, On the nature of the spin glass transition
PDF
, On the nature of the spin glass transition
We recently showed that the two-dimensional Ising spin glass allows for a line of renormalization group fixed points which explains properties observed in numerical studies. We observe that this exact result corresponds to enhancement to a one-generator continuous internal symmetry. This finally explains why no finite temperature transition to a spin glass phase is observed in two dimensions. In more than two dimensions, instead, the continuous symmetry can be broken spontaneously and yields a spin glass order parameter which, for fixed temperature and disorder strength, takes continuous values in an interval. Such a feature is shared by the order parameter of the known mean field solution of the model with infinite-range interactions, which corresponds to infinitely many dimensions.
The following article is
Open access
Dynamics of entanglement fluctuations and quantum Mpemba effect in the
= 1 QSSEP model
Angelo Russotto
et al
J. Stat. Mech.
(2026) 033103
View article
, Dynamics of entanglement fluctuations and quantum Mpemba effect in the ν = 1 QSSEP model
PDF
, Dynamics of entanglement fluctuations and quantum Mpemba effect in the ν = 1 QSSEP model
We study the out-of-equilibrium dynamics of entanglement fluctuations in the
= 1 quantum symmetric simple exclusion process, a free-fermion chain with hopping amplitudes that are stochastic in time but homogeneous in space. Previous work showed that the average entanglement growth after a quantum quench can be explained in terms of pairs of entangled quasiparticles performing random walks, leading to diffusive entanglement spreading. By incorporating the noise-induced statistical correlations between the quasiparticles, we extend this description to the full-time probability distribution of the entanglement entropy. Our generalized quasiparticle picture allows us to compute the average time evolution of a generic function of the reduced density matrix of a subsystem. We also apply our result to the entanglement asymmetry. This allows us to investigate the restoration of particle-number symmetry in the dynamics from initial states with no well-defined particle number. Regarding the possible existence of the quantum Mpemba effect, our analysis indicates that its occurrence is an extremely fine-tuned phenomenon, requiring very specific conditions and therefore being rather difficult to observe in practice.
The following article is
Open access
Coarse-graining nonequilibrium diffusions with Markov chains
Ramón Nartallo-Kaluarachchi
et al
J. Stat. Mech.
(2026) 033205
View article
, Coarse-graining nonequilibrium diffusions with Markov chains
PDF
, Coarse-graining nonequilibrium diffusions with Markov chains
We investigate nonequilibrium steady-state dynamics in both continuous- and discrete-state stochastic processes. Our analysis focuses on planar diffusion dynamics and their coarse-grained approximations by discrete-state Markov chains. Using finite-volume approximations, we derive an approximate master equation directly from the underlying diffusion and show that this discretisation preserves key features of the nonequilibrium steady-state. In particular, we show that the entropy production rate (EPR) of the approximation converges as the number of discrete states goes to the limit. These results are illustrated with analytically solvable diffusions and numerical experiments on nonlinear processes, demonstrating how this approach can be used to explore the dependence of EPR on model parameters. Finally, we address the problem of inferring discrete-state Markov models from continuous stochastic trajectories. We show that discrete-state models significantly underestimate the true EPR. However, we also show that they can provide tests to determine if a stationary planar diffusion is out of equilibrium. This property is illustrated with both simulated data and empirical trajectories from schooling fish.
The following article is
Open access
Classification of diffusion processes in dimension
via the Carleman approach with applications to models involving additive, multiplicative, or square-root noises
Cécile Monthus
J. Stat. Mech.
(2026) 033204
View article
, Classification of diffusion processes in dimension d via the Carleman approach with applications to models involving additive, multiplicative, or square-root noises
PDF
, Classification of diffusion processes in dimension d via the Carleman approach with applications to models involving additive, multiplicative, or square-root noises
The Carleman approach is a popular method in the field of deterministic classical dynamics for replacing a finite number
of nonlinear differential equations by an infinite-dimensional linear system. Here, this approach is applied to a system of
stochastic differential equations for
when the forces and the diffusion-matrix elements are polynomials, to write the linear system governing the dynamics of the averaged values
labeled by the
integers
. The natural decomposition of the Carleman matrix into blocks associated with the global degree
is useful to identify the models with the simplest spectral decompositions in the bi-orthogonal basis of right and left eigenvectors. This analysis is then applied to models with a single noise per coordinate, which can be either additive or multiplicative or square root or with two types of noise per coordinate, with many examples in dimensions
. In
= 1, the Carleman matrix governing the dynamics of the moments
is diagonal for the geometric Brownian motion, whereas it is lower triangular for the family of Pearson diffusions containing the Ornstein–Uhlenbeck and the Square–Root processes, as well as the Kesten, the Fisher–Snedecor, and the Student processes that converge toward steady states with power-law tails. In dimension
= 2, the Carleman matrix governing the dynamics of the correlations
has a natural decomposition into blocks associated to the global degree
, and we discuss the simplest models where the Carleman matrix is either block-diagonal, block-lower-triangular, or block-upper-triangular.
The following article is
Open access
Thermal Casimir effect in the spin–orbit coupled Bose gas
Marek Napiórkowski and Pawel Jakubczyk
J. Stat. Mech.
(2026) 033102
View article
, Thermal Casimir effect in the spin–orbit coupled Bose gas
PDF
, Thermal Casimir effect in the spin–orbit coupled Bose gas
We study the thermal Casimir effect in ideal Bose gases with spin–orbit (S–O) coupling of Rashba type below the critical temperature for Bose–Einstein condensation. In contrast to the standard situation involving no S–O coupling, the system exhibits long-ranged Casimir forces in both two and three dimensions (
= 2 and
= 3). We identify the relevant scaling variable involving the ratio
of the separation between the confining walls
and the S–O coupling magnitude
. We derive and discuss the corresponding scaling functions for the Casimir energy. In all the considered cases, the resulting Casimir force is attractive and the S–O coupling
has impact on its magnitude. In
= 3 the exponent governing the decay of the Casimir force becomes modified by the presence of the S–O coupling, and its value depends on the orientation of the confining walls relative to the plane defined by the Rashba coupling. In
= 2 the obtained Casimir force displays a singular behavior in the limit of vanishing
More Open Access articles
Fast unfolding of communities in large networks
Vincent D Blondel
et al
J. Stat. Mech.
(2008) P10008
View article
, Fast unfolding of communities in large networks
PDF
, Fast unfolding of communities in large networks
We propose a simple method to extract the community structure of large networks. Our
method is a heuristic method that is based on modularity optimization. It is shown to
outperform all other known community detection methods in terms of computation time.
Moreover, the quality of the communities detected is very good, as measured by the
so-called modularity. This is shown first by identifying language communities in a Belgian
mobile phone network of 2 million customers and by analysing a web graph of 118 million
nodes and more than one billion links. The accuracy of our algorithm is also verified on ad
hoc modular networks.
Entanglement entropy and quantum field theory
Pasquale Calabrese and John Cardy
J. Stat. Mech.
(2004) P06002
View article
, Entanglement entropy and quantum field theory
PDF
, Entanglement entropy and quantum field theory
We carry out a systematic study of entanglement entropy in relativistic
quantum field theory. This is defined as the von Neumann entropy
= −Tr ρ
logρ
corresponding to the reduced density matrix
of a subsystem
. For the
case of a 1+1-dimensional critical system, whose continuum limit is a conformal field theory with central charge
, we re-derive the result
of Holzhey
et al
when
is a finite interval of length
in an infinite system, and extend it to many other cases: finite systems, finite temperatures, and when
consists of an arbitrary number of disjoint intervals. For such a
system away from its critical point, when the correlation length
is large but finite, we show that
, where
is the number of boundary points of
These results are verified for a free massive field theory, which is also used to confirm a scaling ansatz
for the case of finite size off-critical systems, and for integrable lattice models, such as the Ising and
XXZ
models, which are solvable by corner transfer matrix methods. Finally the free field
results are extended to higher dimensions, and used to motivate a scaling form for
the singular part of the entanglement entropy near a quantum phase transition.
Evolution of entanglement entropy in one-dimensional systems
Pasquale Calabrese and John Cardy
J. Stat. Mech.
(2005) P04010
View article
, Evolution of entanglement entropy in one-dimensional systems
PDF
, Evolution of entanglement entropy in one-dimensional systems
We study the unitary time evolution of the entropy of entanglement of a one-dimensional
system between the degrees of freedom in an interval of length
and its complement, starting from a pure state which is not an eigenstate of the
Hamiltonian. We use path integral methods of quantum field theory as well as explicit
computations for the transverse Ising spin chain. In both cases, there is a maximum speed
of propagation of signals. In general the entanglement entropy increases linearly with time
up to
, after which it saturates at a value proportional to
, the coefficient depending on the initial state. This behaviour may be understood as a
consequence of causality.
An area law for one-dimensional quantum systems
M B Hastings
J. Stat. Mech.
(2007) P08024
View article
, An area law for one-dimensional quantum systems
PDF
, An area law for one-dimensional quantum systems
We prove an area law for the entanglement entropy in gapped one-dimensional quantum
systems. The bound on the entropy grows surprisingly rapidly with the correlation
length; we discuss this in terms of properties of quantum expanders and present
a conjecture on matrix product states which may provide an alternate way of
arriving at an area law. We also show that, for gapped, local systems, the bound on
Von Neumann entropy implies a bound on Rényi entropy for sufficiently large
α<1
and implies the ability to approximate the ground state by a matrix product
state.
Comparing community structure identification
Leon Danon
et al
J. Stat. Mech.
(2005) P09008
View article
, Comparing community structure identification
PDF
, Comparing community structure identification
We compare recent approaches to community structure identification in terms of sensitivity
and computational cost. The recently proposed modularity measure is revisited and the
performance of the methods as applied to
ad hoc
networks with known community
structure, is compared. We find that the most accurate methods tend to be more
computationally expensive, and that both aspects need to be considered when choosing a
method for practical purposes. The work is intended as an introduction as well
as a proposal for a standard benchmark test of community detection methods.
ConViT: improving vision transformers with soft convolutional inductive biases
Stéphane d’Ascoli
et al
J. Stat. Mech.
(2022) 114005
View article
, ConViT: improving vision transformers with soft convolutional inductive biases
PDF
, ConViT: improving vision transformers with soft convolutional inductive biases
Convolutional architectures have proven to be extremely successful for vision tasks. Their hard inductive biases enable sample-efficient learning, but come at the cost of a potentially lower performance ceiling. Vision transformers rely on more flexible self-attention layers, and have recently outperformed CNNs for image classification. However, they require costly pre-training on large external datasets or distillation from pre-trained convolutional networks. In this paper, we ask the following question: is it possible to combine the strengths of these two architectures while avoiding their respective limitations? To this end, we introduce
gated positional self-attention
(GPSA), a form of positional self-attention which can be equipped with a ‘soft’ convolutional inductive bias. We initialize the GPSA layers to mimic the locality of convolutional layers, then give each attention head the freedom to escape locality by adjusting a
gating parameter
regulating the attention paid to position versus content information. The resulting convolutional-like ViT architecture,
ConViT
, outperforms the DeiT (Touvron
et al
2020 arXiv:
2012.12877
) on ImageNet, while offering a much improved sample efficiency. We further investigate the role of locality in learning by first quantifying how it is encouraged in vanilla self-attention layers, then analyzing how it has escaped in GPSA layers. We conclude by presenting various ablations to better understand the success of the ConViT. Our code and models are released publicly at
Deep double descent: where bigger models and more data hurt
Preetum Nakkiran
et al
J. Stat. Mech.
(2021) 124003
View article
, Deep double descent: where bigger models and more data hurt
PDF
, Deep double descent: where bigger models and more data hurt
We show that a variety of modern deep learning tasks exhibit a ‘double-descent’ phenomenon where, as we increase model size, performance first gets
worse
and then gets better. Moreover, we show that double descent occurs not just as a function of model size, but also as a function of the number of training epochs. We unify the above phenomena by defining a new complexity measure we call the
effective model complexity
and conjecture a generalized double descent with respect to this measure. Furthermore, our notion of model complexity allows us to identify certain regimes where increasing (even quadrupling) the number of train samples actually
hurts
test performance.
Generalized Gibbs ensemble in integrable lattice models
Lev Vidmar and Marcos Rigol
J. Stat. Mech.
(2016) 064007
View article
, Generalized Gibbs ensemble in integrable lattice models
PDF
, Generalized Gibbs ensemble in integrable lattice models
The generalized Gibbs ensemble (GGE) was introduced ten years ago to describe observables in isolated integrable quantum systems after equilibration. Since then, the GGE has been demonstrated to be a powerful tool to predict the outcome of the relaxation dynamics of few-body observables in a variety of integrable models, a process we call generalized thermalization. This review discusses several fundamental aspects of the GGE and generalized thermalization in integrable systems. In particular, we focus on questions such as: which observables equilibrate to the GGE predictions and who should play the role of the bath; what conserved quantities can be used to construct the GGE; what are the differences between generalized thermalization in noninteracting systems and in interacting systems mappable to noninteracting ones; why is it that the GGE works when traditional ensembles of statistical mechanics fail. Despite a lot of interest in these questions in recent years, no definite answers have been given. We review results for the XX model and for the transverse field Ising model. For the latter model, we also report original results and show that the GGE describes spin–spin correlations over the entire system. This makes apparent that there is no need to trace out a part of the system in real space for equilibration to occur and for the GGE to apply. In the past, a spectral decomposition of the weights of various statistical ensembles revealed that generalized eigenstate thermalization occurs in the XX model (hard-core bosons). Namely, eigenstates of the Hamiltonian with similar distributions of conserved quantities have similar expectation values of few-spin observables. Here we show that generalized eigenstate thermalization also occurs in the transverse field Ising model.
Active matter
Sriram Ramaswamy
J. Stat. Mech.
(2017) 054002
View article
, Active matter
PDF
, Active matter
The study of systems with sustained energy uptake and dissipation at the scale of the constituent particles is an area of central interest in nonequilibrium statistical physics. Identifying such systems as a distinct category—Active matter—unifies our understanding of autonomous collective movement in the living world and in some surprising inanimate imitations. In this article I present the active matter framework, briefly recall some early work, review our recent results on single-particle and collective behaviour, including experiments on active granular monolayers, and discuss new directions for the future.
Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
A J Daley
et al
J. Stat. Mech.
(2004) P04005
View article
, Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
PDF
, Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
An algorithm for the simulation of the evolution of slightly entangled quantum states has
been recently proposed as a tool to study time-dependent phenomena in one-dimensional
quantum systems. Its key feature is a time-evolving block-decimation (TEBD) procedure to
identify and dynamically update the relevant, conveniently small, subregion of the
otherwise exponentially large Hilbert space. Potential applications of the TEBD algorithm
are the simulation of time-dependent Hamiltonians, transport in quantum systems far from
equilibrium and dissipative quantum mechanics. In this paper we translate the TEBD
algorithm into the language of matrix product states in order to both highlight and exploit
its resemblances to the widely used density-matrix renormalization-group (DMRG)
algorithms. The TEBD algorithm, being based on updating a matrix product state in
time, is very accessible to the DMRG community and it can be enhanced by
using well-known DMRG techniques, for instance in the event of good quantum
numbers. More importantly, we show how it can be simply incorporated into existing
DMRG implementations to produce a remarkably effective and versatile ‘adaptive
time-dependent DMRG’ variant, that we also test and compare to previous proposals.
Journal links
Submit an article
About the journal
Editorial Board
Editorial information
Author guidelines
Publication charges
News and editorial
Journal collections
Pricing and ordering
Journal information
2004-present
Journal of Statistical Mechanics: Theory and Experiment
doi: 10.1088/issn.1742-5468
Online ISSN: 1742-5468