Journal of Statistical Physics最新文献

{"title":"Characterization of Ergodic Measures of Maximal Entropy for Topologically Transitive Partially Hyperbolic Diffeomorphisms with Compact Center Leaves","authors":"Jorge Crisostomo,&nbsp;Richard Cubas","doi":"10.1007/s10955-026-03702-2","DOIUrl":"10.1007/s10955-026-03702-2","url":null,"abstract":"<div><p>In this paper, we provide an upper bound on the number of maximal entropy ergodic measures with zero Lyapunov exponent for topologically transitive partially hyperbolic diffeomorphisms with compact one-dimensional center leaves on <span>(mathbb {T}^3)</span>. Furthermore, we establish a comprehensive characterization of the support of these measures.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 10","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"Emergent Dynamics of a High-Dimensional Inertial Spin Model on Euclidean Spaces","authors":"Seung-Yeal Ha,&nbsp;Guanghui Jin,&nbsp;Myeonghyeon Kim,&nbsp;Tommaso Ruggeri,&nbsp;Qinghua Xiao","doi":"10.1007/s10955-026-03696-x","DOIUrl":"10.1007/s10955-026-03696-x","url":null,"abstract":"<div><p>We introduce a finite-agent high-dimensional inertial spin (HIS) model which generalizes the classical three-dimensional inertial spin (IS) model and study its emergent behaviors. For the generalization of the IS model, we replace the cross product by multiplication with agent-wise skew-symmetric spin matrices, and identify a new set of constants of motion which are conserved along the proposed model. We provide two frameworks leading to the collective behaviors of the HIS model, yielding qualitative and quantitative emergent dynamics in terms of system parameters and initial data. We also perform a set of numerical simulations and compare them with analytical results.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 10","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"Towards High-Density-Ratio Multiphase Flow: Surface Tension Adjustment in the Three-Dimensional Cumulant Lattice Boltzmann Method","authors":"Jie Kang,&nbsp;Dongyin Wu","doi":"10.1007/s10955-026-03695-y","DOIUrl":"10.1007/s10955-026-03695-y","url":null,"abstract":"<p>This study establishes an asymptotic analysis framework for constructing forcing schemes in the three-dimensional twenty-seven-velocity (D3Q27) cumulant lattice Boltzmann method (LBM). Through multiscale expansion, we develop a forcing scheme that achieves decoupled control of thermodynamic consistency (governed by <span>(lambda )</span>) and surface tension (controlled by <span>(kappa )</span>) within the D3Q27 cumulant LBM for the first time. The proposed forcing scheme modifies the pressure tensor of the Navier–Stokes equations through correction terms derived from asymptotic analysis. Comprehensive validation demonstrate numerical stability through vapor–liquid coexistence curve analysis, static droplet simulations, and wettability simulations. In flat interface simulations, the reduced temperature reaches 0.1 with a corresponding density ratio of <span>(1.53times 10^{19})</span>, which has not been previously achieved in the conventional pseudopotential-based LBM. The proposed forcing scheme enables low-temperature and low-viscosity simulations, making it feasible to investigate spurious currents of the pseudopotential model under a reduced temperature of 0.3 and a viscosity as low as <span>(1times 10^{-5})</span>. Static droplet simulations reveal that as the liquid-phase kinematic viscosity decreases from <span>(1times 10^{-1})</span> to <span>(1times 10^{-3})</span>, maximum spurious velocities exhibit sustained growth, whereas no further augmentation is observed despite continued viscosity reduction to <span>(1times 10^{-5})</span>. In wettability simulations, spurious currents arise near the three-phase contact line at a contact angle of <span>(120^circ )</span>. As the contact angle decreases, these velocity artifacts migrate toward the droplet apex. The developed forcing scheme extends the applicability of the D3Q27 cumulant framework to extreme thermodynamic regimes, thereby establishing a computational foundation to simulate multiphase flows with the pseudopotential model under previously unattainable parameter ranges.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 10","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"Global Stability and Scattering Theory for Non-cutoff Boltzmann Equation with Soft Potentials in the Whole Space: Weak Collision Regime","authors":"Ling-Bing He,&nbsp;Wu-Wei Li","doi":"10.1007/s10955-026-03678-z","DOIUrl":"10.1007/s10955-026-03678-z","url":null,"abstract":"<div><p>A traveling Maxwellian <span>(mathcal {M} = mathcal {M}(t, x, v))</span> represents a traveling wave solution to the Boltzmann equation in the whole space <span>({mathbb R}^3_x)</span>(for the spatial variable). The primary objective of this study is to investigate the global-in-time stability of <span>(mathcal {M})</span> and its associated scattering theory in <span>(L^1_{x,v})</span> space for the non-cutoff Boltzmann equation with soft potentials when the dissipative effects induced by collisions are <i>weak</i>. We demonstrate the following results: (i) <span>(mathcal {M})</span> exhibits Lyapunov stability; (ii) The perturbed solution, which is assumed to satisfy the same conservation law as <span>(mathcal {M})</span>, scatters in <span>(L^1_{x,v})</span> space towards a particular traveling wave (with an explicit convergence rate), which may not necessarily be <span>(mathcal {M})</span>. The key elements in the proofs involve the formulation of the <i>Strichartz-Scaled Boltzmann equation</i> (achieved through the Strichartz-type scaling applied to the original equation) and the propagation of analytic smoothness.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 10","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149133378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"Anomalous Transport in the Fermi-Pasta-Ulam-Tsingou Model: A Review and Open Problems","authors":"Stefano Lepri,&nbsp;Roberto Livi,&nbsp;Antonio Politi","doi":"10.1007/s10955-026-03692-1","DOIUrl":"10.1007/s10955-026-03692-1","url":null,"abstract":"<div><p>This review provides an up-to-date account of energy transport in Fermi-Pasta-Ulam-Tsingou (FPUT) chains, a key testbed for nonequilibrium statistical physics. We discuss the transition from the historical puzzle of thermalization to the discovery of anomalous heat transport, where the effective thermal conductivity <span>(kappa )</span> diverges with system size <i>L</i> as <span>(kappa propto L^delta )</span>. The article clarifies the distinction between two universality classes: the FPUT-<span>(alpha beta )</span> model, characterized by <span>(delta = 1/3)</span> and linked to Kardar-Parisi-Zhang (KPZ) physics, and the symmetric FPUT-<span>(beta )</span> model, where numerical and theoretical evidence support <span>(delta = 2/5)</span>. We investigate how finite-size effects—unavoidably induced by the thermostatting protocols— can disguise the asymptotic scaling. Additionally, we analyze the role of conservative noise in preserving hydrodynamic properties and examine how proximity to integrable limits leads to long-lived quasi-particles and, thereby, to diffusive regimes over intermediate spatial scales.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 10","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03692-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149133158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Parametric RDT Approach to Computational Gap of Symmetric Binary Perceptron","authors":"Mihailo Stojnic","doi":"10.1007/s10955-026-03689-w","DOIUrl":"10.1007/s10955-026-03689-w","url":null,"abstract":"<div><p>We study potential presence of statistical-computational gaps (SCG) in symmetric binary perceptrons (SBP) via a parametric utilization of <i>fully lifted random duality theory</i> (fl-RDT) [96]. A structural change from decreasingly to arbitrarily ordered <span>(textbf{c})</span>-sequence (a key fl-RDT parametric component) is observed on the second lifting level and associated with <i>satisfiability</i> (<span>(alpha _c)</span>) – <i>algorithmic</i> (<span>(alpha _a)</span>) constraints density threshold change thereby suggesting a potential existence of a nonzero computational gap <span>(SCG=alpha _c-alpha _a)</span>. The second level estimate is shown to match the theoretical <span>(alpha _c)</span> whereas the <span>(rrightarrow infty )</span> level one is proposed to correspond to <span>(alpha _a)</span>. For example, for the canonical SBP (<span>(kappa =1)</span> margin) we obtain <span>(alpha _capprox 1.8159)</span> on the second and <span>(alpha _aapprox 1.6021)</span> (with converging tendency towards <span>(sim 1.59)</span> range) on the seventh level. Our propositions remarkably well concur with recent literature: (<b><i>i</i></b>) in [20] local entropy replica approach predicts <span>(alpha _{LE}approx 1.58)</span> as the onset of clustering defragmentaion (presumed driving force behind locally improving algorithms failures); <b><i>(ii)</i></b> in <span>(alpha rightarrow 0)</span> regime we obtain on the third lifting level <span>(kappa approx 1.2385sqrt{frac{alpha _a}{-log left( alpha _a right) }})</span> which qualitatively matches overlap gap property (OGP) based predictions of [43] and identically matches local entropy based predictions of [24]; <b><i>(iii)</i></b> <span>(textbf{c})</span>-sequence ordering change phenomenology mirrors the one observed in asymmetric binary perceptron (ABP) in [101] and the negative Hopfield model in [99]; and <b><i>(iv)</i></b> as in [99, 101], we here design a CLuP based algorithm whose practical performance closely matches proposed theoretical predictions.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 10","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149133024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 Existence of Full Dimensional KAM Tori for Infinite Dimensional Hamiltonian Systems Without External Parameters","authors":"Hongzi Cong,&nbsp;Zhenwei Liu,&nbsp;Zhihan Zhang,&nbsp;Juan Zhao","doi":"10.1007/s10955-026-03701-3","DOIUrl":"10.1007/s10955-026-03701-3","url":null,"abstract":"<div><p>We prove that, for any fixed potential <i>V</i>, there are plenty of full-dimensional KAM tori in infinite-dimensional Hamiltonian systems with short-range interactions.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 10","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149034495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"On the Mean-Field Limit for the Vlasov-Poisson System","authors":"Manuela Feistl-Held,&nbsp;Peter Pickl","doi":"10.1007/s10955-026-03687-y","DOIUrl":"10.1007/s10955-026-03687-y","url":null,"abstract":"<div><p>We present a probabilistic proof of the Mean-field limit and propagation of chaos of a classical N-particle system in three dimensions with Coulomb interaction force of the form <span>(f^N(q)=pm frac{q}{|q|^3})</span> and <i>N</i>-dependent cut-off at <span>(|q|&gt;N^{-frac{5}{12}+sigma })</span> where <span>(sigma &gt;0)</span> can be chosen arbitrarily small. This cut-off size is much smaller than the typical distance to the nearest neighbour. In particular, for typical initial data, we show convergence of the Newtonian trajectories to the characteristics of the Vlasov-Poisson system. The proof is based on a Grönwall estimate for the maximal distance between the exact microscopic dynamics and the approximate Mean-field dynamics. Thus our result leads to a derivation of the Vlasov-Poisson equation from the microscopic <i>N</i>-particle dynamics with force term arbitrary close to the physically relevant Coulomb force.\u0000</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 10","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03687-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148986865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Hydrodynamics of the Fermi–Pasta–Ulam–Tsingou Chain","authors":"Shubhadeep Chakraborty,&nbsp;Abhishek Dhar","doi":"10.1007/s10955-026-03690-3","DOIUrl":"10.1007/s10955-026-03690-3","url":null,"abstract":"<div><p>We provide a pedagogical review of the hydrodynamics of the FPUT chain. There are three hydrodynamic fields corresponding to the conservation of mass, momentum and energy. We provide physically motivated derivations of the hydrodynamic equations at the levels of Euler and then Navier–Stokes–Fourier. Next we consider examples to test as to how successful the hydrodynamic description is in predicting the observed time evolution of nonequilibrium initial conditions such as domain walls and blasts. We find that in some cases there is good agreement of microscopic simulations with predictions from the Euler equations while, in several other cases, there is significant departure from the Euler predictions suggesting that the role of dissipation and noise is important in general.\u0000</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 10","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148986867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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":"Elephant Random Walk on the Infinite Dihedral Group (mathbb {Z}_2 * mathbb {Z}_2)","authors":"Soumendu Sundar Mukherjee,&nbsp;Himasish Talukdar","doi":"10.1007/s10955-026-03683-2","DOIUrl":"10.1007/s10955-026-03683-2","url":null,"abstract":"<div><p>Elephant random walks were studied recently in [10] on the groups <span>(mathbb {Z}^{*d_1} * mathbb {Z}_2^{*d_2})</span> whose Cayley graphs are infinite <i>d</i>-regular trees with <span>(d = 2d_1 + d_2)</span>. It was found that for <span>(d ge 3)</span>, the elephant walk is ballistic with the same asymptotic speed <span>(frac{d - 2}{d})</span> as the simple random walk and the memory parameter appears only in the rate of convergence to the limiting speed. In the <span>(d = 2)</span> case, there are two such groups, both having the bi-infinite path as their Cayley graph. For <span>((d_1, d_2) = (1, 0))</span>, the walk is the usual elephant random walk on <span>(mathbb {Z})</span>, which exhibits anomalous diffusion. In this article, we study the other case, namely <span>((d_1, d_2) = (0, 2))</span>, which corresponds to the infinite dihedral group <span>(D_infty cong mathbb {Z}_2 * mathbb {Z}_2)</span>. Unlike the classical ERW on <span>(mathbb {Z})</span>, which is a time-inhomogeneous Markov chain, the ERW on <span>(D_{infty })</span> is non-Markovian. We show that the first and second order behaviours of the <i>signed location</i> of the walker agree with those of the simple symmetric random walk on <span>(mathbb {Z})</span>, with the memory parameter essentially manifesting itself via a lower order correction term that can be written as an explicit functional of the elephant walk on <span>(mathbb {Z})</span>. Our result demonstrates that unlike the simple random walk, the elephant walk is sensitive to local algebraic relations. Indeed, although <span>(D_{infty })</span> is virtually abelian, containing <span>(mathbb {Z})</span> as a finite-index subgroup, the involutive nature of its generators effectively neutralises memory, thereby ruling out any potential superdiffusive behaviour, in contrast to the superdiffusion observed on its abelian cousin <span>(mathbb {Z})</span>.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 10","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148986866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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}