Journal of Statistical Physics最新文献

{"title":"On the Large Amplitude Solution of the Boltzmann equation with Large External Potential and Boundary Effects","authors":"Jong-in Kim,&nbsp;Donghyun Lee","doi":"10.1007/s10955-025-03459-0","DOIUrl":"10.1007/s10955-025-03459-0","url":null,"abstract":"<div><p>The Boltzmann equation is a fundamental equation in kinetic theory that describes the motion of rarefied gases. In this study, we examine the Boltzmann equation within a <span>(C^{1})</span> bounded domain, subject to a large external potential <span>(Phi (x))</span> and diffuse reflection boundary conditions. Initially, we prove the asymptotic stability of small perturbations near the local Maxwellian <span>(mu _{E}(x,v))</span>. Subsequently, we demonstrate the asymptotic stability of large amplitude solutions with initial data that is arbitrarily large in (weighted) <span>(L^{infty })</span>, but sufficiently small in the sense of relative entropy. Specifically, we extend the results for large amplitude solutions of the Boltzmann equation (with or without external potential) [10,11,12, 23] to scenarios involving significant external potentials [19, 28] under diffuse reflection boundary conditions.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 6","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162383","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":"Exact Potts/Tutte Polynomials for Hammock Chain Graphs","authors":"Yue Chen,&nbsp;Robert Shrock","doi":"10.1007/s10955-025-03457-2","DOIUrl":"10.1007/s10955-025-03457-2","url":null,"abstract":"<div><p>We present exact calculations of the <i>q</i>-state Potts model partition functions and the equivalent Tutte polynomials for chain graphs comprised of <i>m</i> repeated hammock subgraphs <span>(H_{e_1,...,e_r})</span> connected with line graphs of length <span>(e_g)</span> edges, such that the chains have open or cyclic boundary conditions (BC). Here, <span>(H_{e_1,...,e_r})</span> is a hammock (series-parallel) subgraph with <i>r</i> separate paths along “ropes” with respective lengths <span>(e_1, ..., e_r)</span> edges, connecting the two end vertices. We denote the resultant chain graph as <span>(G_{{e_1,...,e_r},e_g,m;BC})</span>. We discuss special cases, including chromatic, flow, and reliability polynomials. In the case of cyclic boundary conditions, the zeros of the Potts partition function in the complex <i>q</i> function accumulate, in the limit <span>(m rightarrow infty )</span>, onto curves forming a locus <span>(mathcal{B})</span>, and we study this locus.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 6","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162384","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":"Spatio-Temporal Fluctuations in the Passive and Active Riesz Gas on the Circle","authors":"Léo Touzo,&nbsp;Pierre Le Doussal,&nbsp;Grégory Schehr","doi":"10.1007/s10955-025-03452-7","DOIUrl":"10.1007/s10955-025-03452-7","url":null,"abstract":"<div><p>We consider a periodic version of the Riesz gas consisting of <i>N</i> classical particles on a circle, interacting via a two-body repulsive potential which behaves locally as a power law of the distance, <span>(sim g/|x|^s)</span> for <span>(s&gt;-1)</span>. Long range (LR) interactions correspond to <span>(s&lt;1)</span>, short range (SR) interactions to <span>(s&gt;1)</span>, while the cases <span>(s=0)</span> and <span>(s=2)</span> describe the well-known log-gas and the Calogero–Moser (CM) model respectively. We study the fluctuations of the positions around the equally spaced crystal configuration, both for Brownian particles—passive noise—and for run-and-tumble particles (RTP)—active noise. We focus on the weak noise regime where the equations of motion can be linearized, and the fluctuations can be computed using the Hessian matrix. We obtain exact expressions for the space-time correlations, both at the macroscopic and microscopic scale, for <span>(N gg 1)</span> and at fixed mean density <span>(rho )</span>. They are characterized by a dynamical exponent <span>(z_s=min (1+s,2))</span>. We also obtain the gap statistics, described by a roughness exponent <span>(zeta _s=frac{1}{2} min (s,1))</span>. For <span>(s&gt;0)</span> in the Brownian case, we find that in a broad window of time, i.e. for <span>(tau =1/(g rho ^{s+2}) ll t ll N^{z_s} tau )</span>, the root mean square displacement of a particle exhibits sub-diffusion as <span>(t^{1/4})</span> for SR as in single-file diffusion, and <span>(t^{frac{s}{2(1+s)}})</span> for LR interactions. Remarkably, this coincides, including the amplitude, with a recent prediction obtained using macroscopic fluctuation theory. These results also apply to RTPs beyond a characteristic time-scale <span>(1/gamma )</span>, with <span>(gamma )</span> the tumbling rate, and a length-scale <span>({hat{g}}^{1/z_s}/rho )</span> with <span>({hat{g}}=1/(2gamma tau ))</span>. Instead, for either shorter times or shorter distances, the active noise leads to a rich variety of static and dynamical regimes, with distinct exponents, for which we obtain detailed analytical results. For <span>(-1&lt;s&lt;0)</span>, the displacements are bounded, leading to true crystalline order at weak noise. The melting transition, recently observed numerically, is discussed in light of our calculation. Finally, we extend our method to the active Dyson Brownian motion and to the active Calogero–Moser model in a harmonic trap, generalizing to finite <span>(gamma )</span> the results of our earlier work. Our results are compared with the mathematics literature whenever possible.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 6","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162386","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 Lower Bound of the Dynamical Critical Exponent of the Ising Model","authors":"Rintaro Masaoka,&nbsp;Tomohiro Soejima,&nbsp;Haruki Watanabe","doi":"10.1007/s10955-025-03456-3","DOIUrl":"10.1007/s10955-025-03456-3","url":null,"abstract":"<div><p>We study the kinetic Ising model under Glauber dynamics and establish an upper bound on the spectral gap for finite systems. This bound implies the critical exponent inequality <span>(z ge 2)</span>, thereby rigorously improving the previously known estimate <span>(z ge 2 - eta )</span>. Our proof relies on the mapping from stochastic processes to frustration-free quantum systems and leverages the Simon–Lieb and Gosset–Huang inequalities.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03456-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144135390","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":"Green’s Function Perspective on the Nonlinear Density Response of Quantum Many-Body Systems","authors":"Jan Vorberger,&nbsp;Tobias Dornheim,&nbsp;Maximilian P. Böhme,&nbsp;Zhandos A. Moldabekov,&nbsp;Panagiotis Tolias","doi":"10.1007/s10955-025-03454-5","DOIUrl":"10.1007/s10955-025-03454-5","url":null,"abstract":"<div><p>We derive equations of motion for higher order density response functions using the theory of thermodynamic Green’s functions. We also derive expressions for the higher order generalized dielectric functions and polarization functions. Moreover, we relate higher order response functions and higher order collision integrals within the Martin–Schwinger hierarchy. We expect our results to be highly relevant to the study of a variety of quantum many-body systems such as matter under extreme temperatures, densities, and pressures.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03454-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144131488","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 Path Method for Non-exponential Ergodicity of Markov Chains and Its Application for Chemical Reaction Systems","authors":"Minjun Kim,&nbsp;Jinsu Kim","doi":"10.1007/s10955-025-03453-6","DOIUrl":"10.1007/s10955-025-03453-6","url":null,"abstract":"<div><p>In this paper, we present criteria for non-exponential ergodicity of continuous-time Markov chains on a countable state space in total variation norm. These criteria can be verified by examining the ratio of transition rates over certain paths. We applied this path method to explore the non-exponential convergence of microscopic biochemical interacting systems. Using reaction network descriptions, we identified special architectures of biochemical systems for non-exponential ergodicity. In essence, we found that reactions forming a cycle in the reaction network can induce non-exponential ergodicity when they significantly dominate other reactions across infinitely many regions of the state space. Interestingly, the special architectures allowed us to construct many detailed balanced and complex balanced biochemical systems that are non-exponentially ergodic. Some of these models are low-dimensional bimolecular systems with few reactions. Thus this work suggests the possibility of discovering or synthesizing stochastic systems arising in biochemistry that possess either detailed balancing or complex balancing and slowly converge to their stationary distribution.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 6","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144125520","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":"Polynomial Escape Rates via Maximal Large Deviations","authors":"Yaofeng Su","doi":"10.1007/s10955-025-03455-4","DOIUrl":"10.1007/s10955-025-03455-4","url":null,"abstract":"<div><p>In this short note, we propose a new and short approach to polynomial escape rates, which can be applied to various open systems with intermittency. The tool of our approach is the maximal large deviations developed in [5].</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03455-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143949655","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":"Exact Calculation of the Large Deviation Function for k-nary Coalescence","authors":"R. Rajesh,&nbsp;V. Subashri,&nbsp;Oleg Zaboronski","doi":"10.1007/s10955-025-03412-1","DOIUrl":"10.1007/s10955-025-03412-1","url":null,"abstract":"<div><p>We study probabilities of rare events in the general coalescence process, <span>(kArightarrow ell A)</span>, where <span>(k&gt;ell )</span>. For arbitrary <span>(k, ell )</span>, by rewriting these probabilities in terms of an effective action, we derive the large deviation function describing the probability of finding <i>N</i> particles at time <i>t</i>, when starting with <i>M</i> particles initially. Additionally, the most probable trajectory corresponding to a fixed rare event is derived.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03412-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143932330","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 Analysis for Canonical Gibbs Measures","authors":"Christian Hirsch,&nbsp;Martina Petráková","doi":"10.1007/s10955-025-03451-8","DOIUrl":"10.1007/s10955-025-03451-8","url":null,"abstract":"<div><p>In this paper, we present a large-deviation theory developed for functionals of canonical Gibbs processes, i.e., Gibbs processes with respect to the binomial point process. We study the regime of a fixed intensity in a sequence of increasing windows. Our method relies on the traditional large-deviation result for local bounded functionals of Poisson point processes noting that the binomial point process is obtained from the Poisson point process by conditioning on the point number. Our main methodological contribution is the development of coupling constructions allowing us to handle delicate and unlikely pathological events. The presented results cover three types of Gibbs models — a model given by a bounded local interaction, a model given by a non-negative possibly unbounded increasing local interaction and the hard-core interaction model. The derived large deviation principle is formulated for the distributions of individual empirical fields driven by canonical Gibbs processes, with its special case being a large deviation principle for local bounded observables of the canonical Gibbs processes. We also consider unbounded non-negative increasing local observables, but the price for treating this more general case is that we only get large-deviation bounds for the tails of such observables. Our primary setting is the one with periodic boundary condition, however, we also discuss generalizations for different choices of the boundary condition.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03451-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143919034","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":"Scale-dependent elasticity as a probe of universal heterogeneity in equilibrium amorphous solids","authors":"Boli Zhou,&nbsp;Rafael Hipolito,&nbsp;Paul M. Goldbart","doi":"10.1007/s10955-025-03450-9","DOIUrl":"10.1007/s10955-025-03450-9","url":null,"abstract":"<div><p>The equilibrium amorphous solid state—formed, <i>e.g.</i>, by adequately randomly crosslinking the constituents of a macromolecular fluid—is a heterogeneous state characterized by a universal distribution of particle localization lengths. Near to the crosslink-density-controlled continuous amorphous-solidification transition, this distribution obeys a scaling form: it has a single peak at a lengthscale that diverges (along with the width of the distribution) as the transition is approached. The modulus controlling macroscale elastic shear deformations of the amorphous solid does not depend on the distribution of localization lengths. However, it is natural to anticipate that for deformations at progressively shorter lengthscales—mesoscale deformations—the effective modulus exhibits a scale-dependence, softening as the deformation lengthscale is reduced. This is because an increasing fraction of the localized particles are, in effect, liquid-like at the deformation lengthscale, and therefore less effective at contributing to the elastic response. In this Paper, the relationship between the distribution of localization lengths and the scale-dependent elastic shear modulus is explored. Following a discussion of intuitive expectations for the scale-dependent elasticity in the amorphous solid state, it is shown, within the setting of a replica mean-field theory, that the effective modulus does indeed exhibit scale-dependent softening. Through this softening, mesoscale elasticity provides a probe of the heterogeneity of the state as characterized by the distribution of localization lengths. In particular, the response to short-lengthscale elastic deformations is shown to shed light on the behavior of the universal localization-length distribution at short localization lengths. Certain experimental techniques that have the potential to yield information specifically about the mesoscale structure and elasticity of amorphous solid states are discussed.\u0000</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 5","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03450-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143913841","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}