Journal of Statistical Physics最新文献

{"title":"Exponential mixing for the stochastic Kuramoto-Sivashinsky equation on the 1D torus","authors":"Peng Gao,&nbsp;Hung D. Nguyen","doi":"10.1007/s10955-026-03669-0","DOIUrl":"10.1007/s10955-026-03669-0","url":null,"abstract":"<div><p>In this paper, we study the large-time behaviors of the Kuramoto-Sivashinsky equation (KSE) on the 1D torus while being subjected to random perturbation via additive Gaussian noise. It is well-known that under suitable assumptions on the stochastic forcing, the KSE admits a unique invariant probability measure. In this work, we make further progress on the topic of ergodicity by addressing the issue of convergence rate toward equilibrium. In comparison with the previous results, we can prove that the unique invariant probability measure is exponentially attractive and smallness condition of anti-diffusion coefficient is not necessary here. The proof relies on a coupling argument while making use of Lyapunov functions motivated by those of deterministic equations.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 8","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148613516","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":"A Generalized Telegraph Process with Resetting to the Origin Driven by Bernoulli Trials","authors":"Antonio Di Crescenzo,&nbsp;Antonella Iuliano,&nbsp;Gabriella Verasani","doi":"10.1007/s10955-026-03670-7","DOIUrl":"10.1007/s10955-026-03670-7","url":null,"abstract":"<div><p>We study a finite-velocity random motion on the real line with alternating velocities <span>(-v)</span> and <i>c</i>, subject to stochastic resetting to the origin. At each velocity-switching epoch, a Bernoulli trial determines whether the particle is instantaneously reset to the origin with probability <span>(theta )</span> or it continues its motion with the opposite velocity with probability <span>(1-theta )</span>. The resulting reset times form a renewal process. We derive the probability distributions of the position-velocity process when the intertimes between consecutive velocity changes have identical (i) exponential distribution, and (ii) Erlang-2 distribution. We also obtain explicit expressions for the moments of the position process and, in case (i), the mean-square distance between the process with resetting and an independent counterpart without resetting. We further characterize the stationary distribution, expressing it in terms of the asymptotic average of the local time of the position process. Finally, we investigate the limiting behavior of the position density under a Kac-type scaling. In both cases (i) and (ii), the position density, conditioned on random initial velocity, converges to that of the Brownian motion with Poisson resetting.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 8","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03670-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466178","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":"Strong solutions and decay estimates for the incompressible Vlasov-MHD system","authors":"Fucai Li,&nbsp;Jinkai Ni,&nbsp;Man Wu","doi":"10.1007/s10955-026-03660-9","DOIUrl":"10.1007/s10955-026-03660-9","url":null,"abstract":"<div><p>In this paper, we study strong solutions and decay estimates for an incompressible Vlasov-magnetohydrodynamic (Vlasov-MHD) model arising in magnetized plasmas. This model consists of the Vlasov equation and the incompressible MHD equations, which interact mutually through the Lorentz force. It can be readily verified that the system has two equilibria: <span>((bar{f},bar{u},bar{B})=(0,0,0))</span> and <span>(( tilde{f},tilde{u},tilde{B})=((2pi )^{- frac{3}{2}}e^{- frac{|v|^2}{2}},0,0))</span>. For any prescribed time interval, we establish the existence and uniqueness of strong solutions under appropriately small initial perturbations that depend on the length of the interval. In both the whole-space and periodic settings, we further derive the corresponding decay estimates for the fluid velocity and magnetic field over the interval of existence. The primary difficulty stems from the lack of drag-type or Fokker–Planck dissipation in the kinetic equation, along with the trilinear coupling generated by the Lorentz force. To address this issue, we combine the characteristic method, support propagation for the kinetic component, refined energy estimates, and Fourier analysis.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 8","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466177","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":"Exponentially slow Mixing arising from Entropic Repulsion in p-SOS model","authors":"Seokun Choi","doi":"10.1007/s10955-026-03661-8","DOIUrl":"10.1007/s10955-026-03661-8","url":null,"abstract":"<div><p>We investigate the Glauber dynamics of the generalized (2+1)-dimensional <i>p</i>-SOS model(<span>(1&lt;p&lt;infty )</span>) under a hard floor constraint. This setting induces entropic repulsion: the integer-valued interface height is forced to remain above the wall and consequently rises to a typical height <i>H</i>(<i>p</i>, <i>L</i>) that depends on both the parameter <i>p</i> and the lattice size <i>L</i>. The phenomenon of entropic repulsion has been extensively studied in a variety of random interface models. In the classical SOS model (<span>(p=1)</span>), [8, 9] derived an exponential lower bound for the mixing time, demonstrating that the Glauber dynamics mixes only after an exponentially long time in the low-temperature regime (large <span>(beta )</span>, the inverse temperature). However, beyond this case, no rigorous lower bounds were previously known: even for the widely studied Discrete Gaussian model (<span>(p=2)</span>), the metastable slowdown predicted by the entropic repulsion picture had remained an open problem. On the equilibrium side, [18] obtained sharp large-deviation principles and precise estimates of typical and maximal heights for all <span>(1le p&lt;infty )</span>, but the dynamical consequences of these results had not been established. Our main contribution is to close this gap by proving that exponentially slow(stretched-exponential) mixing arising from entropic repulsion persists throughout the regime <span>(1&lt;p&lt;infty )</span>. Specifically, we establish an exponential lower bound, showing that the mixing time satisfies <span>(tau _{textrm{mix}}ge exp {left( cL^{1-o(1)}right) })</span> for some <span>(c&gt;0)</span> depending on <i>p</i> and <span>(beta )</span>. In addition, we provide a refined metastability analysis, proving that the hitting time of an intermediate level <i>aH</i>(<i>p</i>, <i>L</i>) is at least <span>(exp {left( cL^{a^{d(p)}-o(1)}right) })</span>, where <span>(0&lt;a&lt;1)</span> and <i>d</i>(<i>p</i>) is a positive function depending on <i>p</i>. The proof relies on an extension of the classical Peierls-type contour estimates, originally developed for <span>(p=1)</span>, to the nonlinear <i>p</i>-SOS setting. Taken together, these results demonstrate that entropic repulsion induces uniformly slow mixing across the entire <i>p</i>-SOS family, thereby extending a phenomenon that had previously been established only for <span>(p=1)</span>.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 8","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03661-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466150","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":"Large Deviation Principle for Complex-Valued Fractional Ginzburg-Landau Equations with Nonlinear Noise on Unbounded Domains","authors":"Sangui Zeng,&nbsp;Jianxin Wu,&nbsp;Jianren Long","doi":"10.1007/s10955-026-03652-9","DOIUrl":"10.1007/s10955-026-03652-9","url":null,"abstract":"<div><p>This study focuses on establishing the large deviation principle (LDP) for a complex-valued fractional Ginzburg-Landau equation (GLE) influenced by nonlinear noise over the unbounded domain <span>(mathbb {R}^d)</span>. Initially, we prove the well-posedness of the related deterministic control system and obtain the uniform tail estimates for its solutions. Subsequently, we show that the set of controlled solutions exhibits strong convergence when the controls are equipped with the weak topology. By examining the distributional convergence of stochastic solutions as <span>(varepsilon rightarrow 0)</span>, we rigorously derive the LDP using the weak convergence method. A key challenge arises from the absence of compact Sobolev embeddings in unbounded domains. To address this, uniform tail estimates are introduced, which ensure the tightness of the induced probability measures and the precompactness of control paths. Additionally, the nonlinear drift term <span>((mu + inu )|X|^{p-2}X)</span> is handled under the admissible constraint <span>(|(p-2)nu | le 2mu sqrt{p-1})</span>, guaranteeing uniqueness, continuity, and convergence of solutions. The validity of the results is preserved under the replacement of <span>((-Delta )^alpha )</span> by the classical Laplace operator. Lastly, numerical experiments are conducted to demonstrate the impact of noise intensity on solution behavior and to provide computational confirmation of the LDP.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 8","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148458793","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":"Rigorous Bound on Hydrodynamic Diffusion for Chaotic Open Spin Chains","authors":"Dimitrios Ampelogiannis,&nbsp;Benjamin Doyon","doi":"10.1007/s10955-026-03658-3","DOIUrl":"10.1007/s10955-026-03658-3","url":null,"abstract":"<div><p>The emergence of diffusion is one of the deepest physical phenomena observed in many-body interacting, chaotic systems. But establishing rigorously that correlation functions, say of the spin, expand diffusively, remains one of the most important problems of mathematical physics. We establish for the first time, with Lindbladian evolution, a lower bound on spin diffusion in chaotic, translation-invariant, nearest-neighbor open quantum spin-1/2 chain satisfying a local unitality condition and strong conservation of magnetization. The bound is strictly positive if and only if the local quantum jumps transport spin. Physically, the bound comes from the spreading effects of initial-state macroscopic fluctuations, a mechanism which occurs whenever spin is an interacting ballistic mode. Chaoticity means that the Hilbert space of extensive charges is spanned by magnetization; we expect this to be generic. Our main tool is the Green-Kubo formula, the mathematical technique of projection over quadratically extensive charges, and appropriate correlation decay bounds recently established. Because Lindbladian dynamics is not reversible, the Green-Kubo spin diffusion strength includes a contribution due to irreversibility, which we interpret as encoding the hydrodynamic entropy production that may occur in the forgotten environment. This, we show, vanishes for certain choices of interaction parameters, for which the Lindbladian dynamics becomes reversible. Our methods can be extended to finite or short ranges, higher spins, and other non-Hamiltonian systems such as quantum circuits. As we argue, according to the theory of nonlinear fluctuating hydrodynamics, we further expect these systems to display superdiffusion, and thus have <i>infinite</i> diffusivity; however this appears to still be beyond the reach of mathematical rigor.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 8","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03658-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148459177","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":"A Two-HCIZ Gaussian Matrix Model for Non-Intersecting Brownian Bridges","authors":"Maksim Kosmakov","doi":"10.1007/s10955-026-03663-6","DOIUrl":"10.1007/s10955-026-03663-6","url":null,"abstract":"<div><p>We construct a unitarily invariant Hermitian matrix ensemble whose fixed-time eigenvalue law coincides with the Karlin–McGregor law for non-intersecting Brownian bridges with arbitrary finite multiplicities at both endpoints. This provides an explicit matrix-ensemble realization of the known mixed-type multiple orthogonal polynomial and Riemann–Hilbert description of the general multi-start/multi-end problem. We then derive several exact finite-<i>n</i> consequences of this construction. These include a path-space lift as an orbital Hermitian Brownian bridge and a reduction of the partition function to a single compact HCIZ integral with explicit <i>t</i>-dependence. We also compare the one-sided reduction with the Gaussian external-field ensemble, showing that, although the two ensembles are spectrally equivalent, their angular statistics are different. Finally, we derive fixed-time Schwinger–Dyson identities and associated resolvent relations for the dressed ensemble.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 8","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03663-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148459178","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":"Free Energy Dissipation and a Decomposition of General Jump Diffusions on (mathbb {R}^n) without Detailed Balance","authors":"Shuyuan Fan,&nbsp;Qi Zhang","doi":"10.1007/s10955-026-03667-2","DOIUrl":"10.1007/s10955-026-03667-2","url":null,"abstract":"<div><p>We analyze the thermodynamic structure of jump diffusions combining Brownian and Poisson noise, a class of stochastic dynamics relevant to non-equilibrium statistical physics. For such nonlocal dynamics, the free energy admits a full dissipation formula that decomposes into entropy production and housekeeping heat. A central result is a decomposition of the generator into symmetric and anti-symmetric parts with respect to the invariant measure <span>(rho _textrm{ss})</span>. The symmetric sector corresponds to a reversible dynamics and yields a nonlocal Fisher information governing free-energy decay, whereas the anti-symmetric sector generates a canonical conservative flow that produces circulation but no dissipation. Several numerical examples motivated by intracellular particle transports demonstrate how this decomposition clarifies the structure of non-equilibrium stationary states in jump-driven systems.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 7","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466130","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":"Classification of the Limit Shape for 1+1-Dimensional FPP","authors":"Malte Haßler","doi":"10.1007/s10955-026-03657-4","DOIUrl":"10.1007/s10955-026-03657-4","url":null,"abstract":"<div><p>We introduce a simplified model of planar first passage percolation where weights along vertical edges are deterministic. We show that the limit shape has a flat edge in the vertical direction if and only if the distribution of the horizontal edges has an atom at the infimum of its support. Furthermore, we present bounds on the upper and lower derivative of the time constant.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 7","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465613","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":"Exponential (Phi )-Mixing Implies Exponential (Psi )-Mixing For Markov Fields On Bounded Degree Graphs","authors":"Elias Zimmermann","doi":"10.1007/s10955-026-03630-1","DOIUrl":"10.1007/s10955-026-03630-1","url":null,"abstract":"<div><p>We show that for non-degenerate <i>k</i>-Markovian random fields with finite state space over a bounded degree graph with exponential growth rate <img>, uniform <img>-mixing with exponential decay rate <img> implies uniform <img>-mixing with exponential decay rate <img>. As an application we obtain exponential <img>-mixing for Gibbs fields on regular trees arising from finite range potentials such as the Ising model at low inverse temperature or the Potts model with sufficiently many spin states.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 7","pages":""},"PeriodicalIF":1.1,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03630-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465263","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}