Journal of Statistical Physics最新文献

{"title":"Expected Number of Jumps and the Number of Active Particles in TASEP","authors":"Paweł Hitczenko,&nbsp;Jacek Wesołowski","doi":"10.1007/s10955-025-03483-0","DOIUrl":"10.1007/s10955-025-03483-0","url":null,"abstract":"<div><p>For a TASEP on <span>(mathbb Z)</span> with the step initial condition we identify limits as <span>(trightarrow infty )</span> of the expected total number of jumps until time <span>(t&gt;0)</span> and the expected number of active particles at a time <i>t</i>. We also connect the two quantities proving that non-asymptotically, that is as a function of <span>(t&gt;0)</span>, the latter is the derivative of the former. Our approach builds on asymptotics derived by Rost and intensive use of the fact that the rightmost particle evolves according to the Poisson process.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 8","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03483-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166175","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":"Asymptotic Behavior of the Generalized Derrida–Retaux Recursive Model","authors":"Zenghu Li,&nbsp;Run Zhang","doi":"10.1007/s10955-025-03480-3","DOIUrl":"10.1007/s10955-025-03480-3","url":null,"abstract":"<div><p>We study the max-type recursive model introduced by Hu and Shi (J. Stat. Phys., 2018), which generalizes the model of Derrida and Retaux (J. Stat. Phys., 2014). The class of geometric-type marginal distributions is preserved by the model with geometric offspring distribution. We give some long-time asymptotic expansions of the parameters of the marginal distribution. From the expansions, we derive the asymptotics of the sustainability probability, marginal distribution, first moment and probability generating function.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 8","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165664","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":"Homoenergetic solutions for the Rayleigh-Boltzmann equation: existence of a stationary non-equilibrium solution","authors":"Nicola Miele,&nbsp;Alessia Nota,&nbsp;Juan J. L. Velázquez","doi":"10.1007/s10955-025-03481-2","DOIUrl":"10.1007/s10955-025-03481-2","url":null,"abstract":"<div><p>In this paper we consider a particular class of solutions of the linear Boltzmann-Rayleigh equation, known in the nonlinear setting as homoenergetic solutions. These solutions describe the dynamics of Boltzmann gases under the effect of different mechanical deformations. Therefore, the long-time behaviour of these solutions cannot be described by Maxwellian distributions and it strongly depends on the homogeneity of the collision kernel of the equation.</p><p>Here we focus on the paradigmatic case of simple shear deformations and in the case of cut-off collision kernels with homogeneity <span>(gamma ge 0)</span>, in particular covering the case of Maxwell molecules (i.e. <span>(gamma =0)</span>) and hard potentials with <span>(0le gamma &lt;1)</span>. We first prove a well-posedness result for this class of solutions in the space of non-negative Radon measures and then we rigorously prove the existence of a stationary solution under the non-equilibrium condition which is induced by the presence of the shear deformation. In the case of Maxwell molecules we prove that there is a different behaviour of the solutions for small and large values of the shear parameter.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 7","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143521","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":"Relaxation Time and Topology in 1D O(N) Models","authors":"Pietro Caputo,&nbsp;Sébastien Ott,&nbsp;Assaf Shapira","doi":"10.1007/s10955-025-03475-0","DOIUrl":"10.1007/s10955-025-03475-0","url":null,"abstract":"<div><p>We discuss the relaxation time (inverse spectral gap) of the one dimensional <i>O</i>(<i>N</i>) model, for all <i>N</i> and with two types of boundary conditions. We see how its low temperature asymptotic behavior is affected by the topology. The combination of the space dimension, which here is always 1, the boundary condition (free or periodic), and the spin state <span>({mathbb {S}}^{N-1})</span>, determines the existence or absence of non-trivial homotopy classes in some discrete version. Such non-trivial topology reflects in bottlenecks of the dynamics, creating metastable states that the system exits at exponential times; while when only one homotopy class exists the relaxation time depends polynomially on the temperature. We prove in the one dimensional case that, indeed, the relaxation time is a proxy to the model’s topological properties via the exponential/polynomial dependence on the temperature.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 7","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145142919","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":"Pseudo-RNA with parallel aligned single-strands and periodic base sequence as a new universality class","authors":"Richard Dengler","doi":"10.1007/s10955-025-03477-y","DOIUrl":"10.1007/s10955-025-03477-y","url":null,"abstract":"<div><p>This work investigates a field theory for RNA-like polymers with periodic base sequence GCGCG..., where only single-strands aligned in the same direction form double strands. The field theory is derived from a lattice model that incorporates excluded volume effects, base sequence, and temperature dependent denaturation - renaturation. The artificial directionality leads to a novel universality class, not related to conventional branched polymers and Lee-Yang field theory. This universality class is unstable against natural pairing, where oppositely aligned single-strands form double strands. Near the upper critical dimension <span>(d=6)</span> the denaturation - renaturation transition is a continuous crossover between two <span>(varphi _{n=0}^{4})</span> critical points and the critical point of the new universality class. However, the behavior for <span>(dle 5)</span> remains unclear.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 7","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143000","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":"Bounds on (T_c) in the Eliashberg Theory of Superconductivity. II: Dispersive Phonons","authors":"M. K.-H. Kiessling,&nbsp;B. L. Altshuler,&nbsp;E. A. Yuzbashyan","doi":"10.1007/s10955-025-03468-z","DOIUrl":"10.1007/s10955-025-03468-z","url":null,"abstract":"<div><p>The standard Eliashberg theory of superconductivity is studied, in which the effective electron-electron interactions are modelled as mediated by generally dispersive phonons, with Eliashberg spectral function <span>(alpha ^2!F(omega )ge 0)</span> that is <span>(propto omega ^2)</span> for small <span>(omega &gt;0)</span> and vanishes for large <span>(omega )</span>. The Eliashberg function also defines the electron-phonon coupling strength <span>(lambda := 2 displaystyle int _{mathbb {R}_+}!! frac{alpha ^2!F(omega )}{omega }domega )</span>. Setting <span>({ displaystyle frac{2alpha ^2!F(omega )}{omega }}domega =: lambda P(domega ))</span>, formally defining a probability measure <span>(P(domega ))</span> with compact support, and assuming as usual that the phase transition between normal and superconductivity coincides with the linear stability boundary <span>(mathscr {S}_{!c})</span> of the normal region in the <span>((lambda ,P,T))</span> parameter space against perturbations toward the superconducting region, it is shown that this <i>critical hypersurface</i> <span>(mathscr {S}_{!c})</span> is a graph of a function <span>(Lambda (P,T))</span>. This proves that the normal and the superconducting regions are simply connected. Moreover, it is shown that <span>(mathscr {S}_{!c})</span> is determined by a variational principle: if <span>((lambda ,P,T)in mathscr {S}_{!c})</span>, then <span>(lambda = 1/mathfrak {k}(P,T))</span>, where <span>(mathfrak {k}(P,T)&gt;0)</span> is the largest eigenvalue of a compact self-adjoint operator <span>(mathfrak {K}(P,T))</span> on <span>(ell ^2)</span> sequences that is constructed explicitly in the paper, for all admissible <i>P</i>. Furthermore, given any such <i>P</i>, sufficient conditions on <i>T</i> are stated under which the map <span>(Tmapsto lambda = Lambda (P,T))</span> is invertible. For sufficiently large <span>(lambda )</span> this yields the following: (i) the existence of a critical temperature <span>(T_c)</span> as function of <span>(lambda )</span> and <i>P</i>; (ii) an ordered sequence of lower bounds on <span>(T_c(lambda ,P))</span> that converges to <span>(T_c(lambda ,P))</span>. Also obtained is an upper bound on <span>(T_c(lambda ,P))</span>. Although not optimal, it agrees with the asymptotic form <span>(T_c(lambda ,P) sim C sqrt{langle omega ^2rangle } sqrt{lambda })</span> valid for <span>(lambda sim infty )</span>, given <i>P</i>, though with a constant <i>C</i> that is a factor <span>(approx 2.034)</span> larger than the sharp constant; here, <span>(langle omega ^2rangle := int _{mathbb {R}_+} omega ^2 P(domega ))</span>.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 7","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03468-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145142645","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":"Bounds on (T_c) in the Eliashberg Theory of Superconductivity. III: Einstein Phonons","authors":"M. K.-H. Kiessling,&nbsp;B. L. Altshuler,&nbsp;E. A. Yuzbashyan","doi":"10.1007/s10955-025-03469-y","DOIUrl":"10.1007/s10955-025-03469-y","url":null,"abstract":"<div><p>The dispersionless limit of the standard Eliashberg theory of superconductivity is studied, in which the effective electron-electron interactions are mediated by Einstein phonons of frequency <span>(Omega &gt;0)</span>, equipped with electron-phonon coupling strength <span>(lambda )</span>. The general results on <span>(T_c)</span> for phonons with non-trivial dispersion relation, obtained in a previous paper by the authors, (II), then become amenable to a detailed evaluation. The results are based on the traditional notion that the phase transition between normal and superconductivity coincides with the linear stability boundary <span>(mathscr {S}_{!c})</span> of the normal state region against perturbations toward the superconducting region. The variational principle for <span>(mathscr {S}_{!c})</span>, obtained in (II), simplifies as follows: If <span>((lambda ,Omega ,T)in mathscr {S}_{!c})</span>, then <span>(lambda = 1/mathfrak {h}(varpi ))</span>, where <span>(varpi :=Omega /2pi T)</span>, and where <span>(mathfrak {h}(varpi )&gt;0)</span> is the top eigenvalue of a compact self-adjoint operator <span>(mathfrak {H}(varpi ))</span> on <span>(ell ^2)</span> sequences; <span>(mathfrak {H}(varpi ))</span> is the dispersionless limit <span>(P(domega )rightarrow delta (omega -Omega )domega )</span> of the operator <span>(mathfrak {K}(P,T))</span> of (II). It is shown that when <span>(varpi le sqrt{2})</span>, then the map <span>(varpi mapsto mathfrak {h}(varpi ))</span> is invertible. For sufficiently large <span>(lambda )</span> (<span>(lambda &gt;0.77)</span> will do) this yields the following: (i) the existence of a critical temperature <span>(T_c(lambda ,Omega ) = Omega f(lambda ))</span>; (ii) an ordered sequence of lower bounds on <span>(f(lambda ))</span> that converges to <span>(f(lambda ))</span>. Also obtained is an upper bound on <span>(T_c(lambda ,Omega ))</span>, which is not optimal yet agrees with the asymptotic behavior <span>(T_c(lambda ,Omega ) sim C Omega sqrt{lambda })</span> for large enough <span>(lambda )</span>, given <span>(Omega )</span>, though with a constant <i>C</i> that is a factor <span>(approx 2.034)</span> larger than the optimal constant <span>(frac{1}{2pi }mathfrak {g}(2)^frac{1}{2} =0.1827262477...)</span>, with <span>(mathfrak {g}(gamma )&gt;0)</span> the largest eigenvalue of the compact self-adjoint operator <span>(mathfrak {G}(gamma ))</span> for the <span>(gamma )</span> model, determined rigorously in the first one, (I), of this series of papers on <span>(T_c)</span> by the authors.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 7","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03469-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145142503","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":"The Eigenfunctions of the Transfer Operator for the Dyson Model in a Field","authors":"Mirmukhsin Makhmudov","doi":"10.1007/s10955-025-03476-z","DOIUrl":"10.1007/s10955-025-03476-z","url":null,"abstract":"<div><p>The recent works [5] and [15] have studied the spectral properties of the Dyson model in the absence of an external field. This paper is a continuation of [5] and aims to bridge the gap in the literature by investigating the Dyson model in a field. In this paper, we prove that, for high temperatures or strong magnetic fields, there exists a non-negative, integrable (with respect to the unique half-line Gibbs measure) eigenfunction of the transfer operator for the Dyson model if <span>(alpha in (frac{3}{2},2])</span>. However, unlike in the zeromagnetic- field case, this eigenfunction is not continuous.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 7","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03476-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145142140","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":"Global Thermodynamics for Isothermal Fluids Under Weak Gravity","authors":"Naoko Nakagawa,&nbsp;Shin-ichi Sasa,&nbsp;Takamichi Hirao,&nbsp;Tsuyoshi Shiina,&nbsp;Kyosuke Tachi,&nbsp;Akira Yoshida","doi":"10.1007/s10955-025-03473-2","DOIUrl":"10.1007/s10955-025-03473-2","url":null,"abstract":"<div><p>We develop a formulation of global thermodynamics for equilibrium systems under the influence of weak gravity. The free energy for simple fluids is extended to include a dependence on <span>((T, V, N, mtextit{g}L))</span>, where <i>L</i> represents the vertical system length in the direction of gravity. A central idea in this formulation is to uniquely fix the reference point of the gravitational potential, ensuring a consistent thermodynamic framework. Using this framework, we derive the probability density of thermodynamic quantities, which allows us to define a variational function for determining equilibrium liquid-gas coexistence under gravity when the interface is flat. The resulting free energy landscape, derived from the variational function, reveals the local stability of liquid-gas configurations. Specifically, the liquid phase resides at the lower portion of the system due to gravity, while the inverted configuration (with liquid on top) is also locally stable in this landscape. Furthermore, we characterize the transition between these liquid-gas configurations as a first-order phase transition using the thermodynamic free energy of <span>((T,V,N,mtextit{g}L))</span>. Finally, we validate the predictions of global thermodynamics through molecular dynamics simulations, demonstrating the applicability and accuracy of the proposed framework.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 7","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03473-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145145398","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":"Non-equilibrium Steady States with a Spatial Markov Structure","authors":"Frank Redig,&nbsp;Berend van Tol","doi":"10.1007/s10955-025-03471-4","DOIUrl":"10.1007/s10955-025-03471-4","url":null,"abstract":"<div><p>We investigate the structure of non-equilibrium steady states (NESS) for a class of exactly solvable models in the setting of a chain with left and right reservoirs. Inspired by recent results on the harmonic model Large deviations and additivity principle for the open harmonic process, (2023), (JSP 191(1):10, 2024). we focus on models in which the NESS is a mixture of equilibrium product measures, and where the probability measure which describes the mixture has a spatial Markovian property. We completely characterize the structure of such mixture measures, and show that under natural scaling and translation invariance properties, the only possible mixture measures are coinciding with the Dirichlet process found in Carinci Gioia, Franceschini Chiara, Frassek Rouven, Giardinà Cristian, Redig Frank. Large deviations and additivity principle for the open harmonic process, (2023), in the context of the harmonic model.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 7","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03471-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145144773","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}