Journal of Statistical Physics最新文献

{"title":"Existence and Stability of Non-Equilibrium Steady States of a Weakly Non-Linear Kinetic Fokker-Planck Equation in a Domain","authors":"Josephine Evans,&nbsp;Richard Medina","doi":"10.1007/s10955-026-03604-3","DOIUrl":"10.1007/s10955-026-03604-3","url":null,"abstract":"<div><p>We study a weakly non-linear Fokker-Planck equation with BGK heat thermostats in a spatially bounded domain with conservative Maxwell boundary conditions, presenting a space-dependent accommodation coefficient and a space-dependent temperature on the spatial boundary. The model is based from a problem introduced in [E. A. Carlen, R. Esposito, J. L. Lebowitz, R. Marra, and C. Mouhot.<i> Approach to the steady state in kinetic models with thermal reservoirs at different temperatures.</i> <i>J</i>. Stat. Phys., 172(2):522–543, 2018] where the authors studied the properties of the non-equilibrium steady states for non-linear kinetic Fokker-Planck equations with BGK thermostats in the torus. We generalize those results for bounded domains using the recent results presented in [K. Carrapatoso, P. Gabriel, R. Medina, and S. Mischler. <i>Constructive Krein-Rutman result for kinetic Fokker-Planck equations in a domain</i>, 2024] for the study of general kinetic Fokker-Planck equations with Maxwell boundary conditions. More precisely, in a weakly non-linear regime, we obtain the existence of a non-equilibrium steady state and its stability in the perturbative regime.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147606489","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 Tracy-Widom Distribution at Large Dyson Index","authors":"Alain Comtet,&nbsp;Pierre Le Doussal,&nbsp;Naftali R. Smith","doi":"10.1007/s10955-026-03596-0","DOIUrl":"10.1007/s10955-026-03596-0","url":null,"abstract":"<div><p>We study the Tracy-Widom (TW) distribution <span>(f_beta (a))</span> in the limit of large Dyson index <span>(beta rightarrow +infty )</span>. This distribution describes the fluctuations of the rescaled largest eigenvalue <span>(a_1)</span> of the Gaussian (alias Hermite) ensemble (G<span>(beta )</span>E) of (infinitely) large random matrices. We show that, at large <span>(beta )</span>, its probability density function takes the large deviation form <span>(f_beta (a) sim e^{-beta Phi (a)})</span>. While the typical deviation of <span>(a_1)</span> around its mean is Gaussian of variance <span>(O(1/beta ))</span>, this large deviation form describes the probability of rare events with deviation <i>O</i>(1), and governs the behavior of the higher cumulants. We obtain the rate function <span>(Phi (a))</span> as a solution of a Painlevé II equation. We derive explicit formula for its large argument behavior, and for the lowest cumulants, up to order 4. We compute <span>(Phi (a))</span> numerically for all <i>a</i> and compare with exact numerical computations of the TW distribution at finite <span>(beta )</span>. These results are obtained by applying saddle-point approximations to an associated problem of energy levels <span>(E=-a)</span>, for a random quantum Hamiltonian defined by the stochastic Airy operator (SAO). We employ two complementary approaches: (i) we use the optimal fluctuation method to find the most likely realization of the noise in the SAO, conditioned on its ground-state energy being <i>E</i> (ii) we apply the weak-noise theory to the representation of the TW distribution in terms of a Ricatti diffusion process associated to the SAO. We extend our results to the full Airy point process <span>(a_1&gt;a_2&gt;dots )</span> which describes all edge eigenvalues of the G<span>(beta )</span>E, and correspond to (minus) the higher energy levels of the SAO, obtaining large deviation forms for the marginal distribution of <span>(a_i)</span>, the joint distributions, and the gap distributions.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03596-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147606481","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":"On the Onsager-Machlup Functional of the (Phi ^4)-Measure","authors":"Ioannis Gasteratos,&nbsp;Zachary Selk","doi":"10.1007/s10955-026-03602-5","DOIUrl":"10.1007/s10955-026-03602-5","url":null,"abstract":"<div><p>We investigate the existence of generalised densities for the <span>(Phi ^4_d)</span> <span>((d=1,2,3))</span> measures, in finite volume, through the lens of Onsager-Machlup (OM) functionals. The latter are rigorously defined for measures on metric spaces as limiting ratios of small ball probabilities. In one dimension, we show that the standard OM functional of the <span>(Phi ^4_1)</span> measure coincides with the <span>(Phi ^4)</span> action as expected. In two dimensions, we show that OM functionals of the <span>(P(Phi )_2)</span> measures agree with the corresponding actions, by considering “enhanced\" distances, defined with respect to Wick powers of the Gaussian Free Field, which are analogous to rough path metrics. In dimension 3, two natural generalisations of the OM functional are proved to be degenerate. Finally, we recover the <span>(Phi ^4_3)</span> action, under appropriate regularity conditions, by considering joint small radius-large frequency limits.\u0000</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03602-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147607236","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":"Two-Temperature Fluid Models for a Polyatomic Gas Based on Kinetic Theory for Nearly Resonant Collisions","authors":"Kazuo Aoki,&nbsp;Niclas Bernhoff","doi":"10.1007/s10955-026-03597-z","DOIUrl":"10.1007/s10955-026-03597-z","url":null,"abstract":"<div><p>A polyatomic ideal gas with weak interaction between the translational and internal modes is considered. For the purpose of describing the behavior of such a gas, a Boltzmann equation is proposed in the form that the collision integral is a linear combination of inelastic and elastic (or resonant) collisions, and its basic properties are discussed. Then, in the case where the elastic collisions are dominant, fluid dynamic equations of Euler and Navier–Stokes type including two temperatures, i.e., translational and internal temperatures, as well as relaxation terms are systematically obtained by means of the Chapman–Enskog expansion. The obtained equations are different depending on the degree of weakness of the interaction between the translational and internal modes.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03597-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147607350","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 First Passage Problem for a Poisson Counting Process with a Linear Moving Boundary","authors":"Ivan N. Burenev,&nbsp;Michael J. Kearney,&nbsp;Satya N. Majumdar","doi":"10.1007/s10955-026-03600-7","DOIUrl":"10.1007/s10955-026-03600-7","url":null,"abstract":"<div><p>The time to first crossing for the Poisson counting process with respect to a linear moving barrier with offset is a classic problem, although key results remain scattered across the literature and their equivalence is often unclear. Here we present a unified and pedagogical treatment of two approaches: the direct time-domain approach based on path-decomposition techniques and the Laplace-domain approach based on the Pollaczek-Spitzer formula. Beyond streamlining existing derivations and establishing their consistency, we leverage the complementary nature of the two methods to obtain new exact analytical results. Specifically, we derive an explicit large deviation function for the first-passage time distribution in the subcritical regime and closed-form expressions for the conditional mean first-passage time for arbitrary offset. Despite its simplicity, this first crossing process exhibits non-trivial critical behavior and provides a rare example where all the main results of interest can be derived exactly.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03600-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560964","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":"Relative Entropy and Slightly Compressible Navier-Stokes Dynamics of the Boltzmann Equation","authors":"Yuhan Chen,&nbsp;Ning Jiang","doi":"10.1007/s10955-026-03601-6","DOIUrl":"10.1007/s10955-026-03601-6","url":null,"abstract":"<div><p>This paper shows that, in the formal level, the convergence of solutions of Boltzmann equation to solutions of the compressible Navier-Stokes system with small Mach number over the three-dimensional periodic domain <span>(mathbb {T}^3)</span>, using the relative entropy method originated from Bardos, Golse, Levermore [<i>Comm. Pure Appl. Math.</i> <b>46</b> (1993) 667–753] and Yau [<i>Lett. Math. Phys.</i> <b>22</b> (1991) 63–80]. We discuss the evolution of the entropy which is relative to the local Maxwellian governed by the solution of slightly compressible Navier-Stokes system. This characterizes the convergence rate from Boltzmann equation to the incompressible Navier-Stokes system.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561645","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":"Statistical Mechanics of Fluids with Hidden Degrees of Freedom","authors":"Masanari Shimada,&nbsp;Tetsuya J. Kobayashi","doi":"10.1007/s10955-026-03595-1","DOIUrl":"10.1007/s10955-026-03595-1","url":null,"abstract":"<div><p>Although coarse-grained models have been widely used to explain exotic phenomena in complex fluids, such as droplet formation in living cells, these conventional approaches often fail to capture the intricate microscopic degrees of freedom that such fluids inherently possess. In this study, we propose a model that incorporates distinct microscopic degrees of freedom and their interactions, without directly relying on conventional coarse-grained descriptions. By introducing two key assumptions, we show that the system can exhibit equilibrium states characterized by heterogeneous density profiles with finite length scales, resembling those typically associated with non-equilibrium phenomena. These findings highlight the importance of distinguishing between equilibrium states and non-equilibrium steady states in highly complex systems.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560442","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":"Control of a Uniformly Magnetized Plasma with External Electric Fields","authors":"Peiyi Chen,&nbsp;Rogerio Jorge,&nbsp;Qin Li,&nbsp;Yukun Yue","doi":"10.1007/s10955-026-03599-x","DOIUrl":"10.1007/s10955-026-03599-x","url":null,"abstract":"<div><p>Stabilizing plasma dynamics through externally applied electric and magnetic fields is a fundamental control problem. We study this question for a plasma evolving under a uniform external magnetic field. Although the governing dynamics are nonlinear, a linear analysis based on the Laplace-Fourier transform yields actionable insight. In particular, by controlling the location of the roots of the dispersion relation, we propose a general control strategy that restores stability, with the free-streaming solution recovered as a special case. Numerical experiments for Gaussian equilibria and for the Dory-Guest-Harris instability show that the proposed control suppresses the unstable modes and stabilizes the dynamics, in agreement with our theoretical predictions.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 4","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560292","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":"Dynamics of a Bricklayer Model: Multi-Walker Realizations of True Self-Avoiding Motion","authors":"A. C. Maggs","doi":"10.1007/s10955-026-03594-2","DOIUrl":"10.1007/s10955-026-03594-2","url":null,"abstract":"<div><p>We investigate a multi-walker generalization of the true self-avoiding walk, formulated as a bricklayer model where agents collectively build a growing interface. We investigate the coupled partial differential equations that describe the hydrodynamic limit of this process. Stochastic simulations of <i>N</i> walkers confirm these analytic predictions in the large-<i>N</i> limit, revealing a characteristic parabolic density profile. These results provide a continuum description for the dynamics of non-reversible Monte Carlo algorithms, offering insights into the relaxation mechanisms of collective sampling schemes.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03594-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441714","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":"Operator Product Expansions of Derivative Fields in the Sine-Gordon Model","authors":"Alex Karrila,&nbsp;Tuomas Virtanen,&nbsp;Christian Webb","doi":"10.1007/s10955-026-03585-3","DOIUrl":"10.1007/s10955-026-03585-3","url":null,"abstract":"<div><p>In this article, we initiate the study of operator product expansions (OPEs) for the sine-Gordon model. For simplicity, we focus on the model below the first threshold of collapse (<span>(beta &lt;4pi )</span>) and on the singular terms in OPEs of derivative-type fields <span>(partial varphi )</span> and <span>(bar{partial }varphi )</span>. We prove that compared to corresponding free field OPEs, the sine-Gordon OPEs develop logarithmic singularities and generate Wick ordered exponentials. Our approach for proving the OPEs relies heavily on Onsager-type inequalities and associated moment bounds for GFF correlation functions involving Wick ordered exponentials of the free field.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"193 3","pages":""},"PeriodicalIF":1.2,"publicationDate":"2026-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-026-03585-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147440870","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}