Journal of Statistical Physics最新文献

{"title":"Exponential Ergodicity for the Stochastic Hyperbolic Sine-Gordon Equation on the Circle","authors":"Kihoon Seong","doi":"10.1007/s10955-024-03347-z","DOIUrl":"10.1007/s10955-024-03347-z","url":null,"abstract":"<div><p>In this paper, we show that the Gibbs measure of the stochastic hyperbolic sine-Gordon equation on the circle is the unique invariant measure for the Markov process. Moreover, the Markov transition probabilities converge exponentially fast to the unique invariant measure in a type of 1-Wasserstein distance. The main difficulty comes from the fact that the hyperbolic dynamics does not satisfy the strong Feller property even if sufficiently many directions in a phase space are forced by the space-time white noise forcing. We instead establish that solutions give rise to a Markov process whose transition semigroup satisfies the asymptotic strong Feller property and convergence to equilibrium in a type of Wasserstein distance.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 10","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411206","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":"Heat Transport Through an Open Coupled Scalar Field Theory Hosting Stability-to-Instability Transition","authors":"T. R. Vishnu,&nbsp;Dibyendu Roy","doi":"10.1007/s10955-024-03341-5","DOIUrl":"10.1007/s10955-024-03341-5","url":null,"abstract":"<div><p>We investigate heat transport through a one-dimensional open coupled scalar field theory, depicted as a network of harmonic oscillators connected to thermal baths at the boundaries. The non-Hermitian dynamical matrix of the network undergoes a stability-to-instability transition at the exceptional points as the coupling strength between the scalar fields increases. The open network in the unstable regime, marked by the emergence of inverted oscillator modes, does not acquire a steady state, and the heat conduction is then unbounded for general bath couplings. In this work, we engineer a unique bath coupling where a single bath is connected to two fields at each edge with the same strength. This configuration leads to a finite steady-state heat conduction in the network, even in the unstable regime. We also study general bath couplings, e.g., connecting two fields to two separate baths at each boundary, which shows an exciting signature of approaching the unstable regime for massive fields. We derive analytical expressions for high-temperature classical heat current through the network for different bath couplings at the edges and compare them. Furthermore, we determine the temperature dependence of low-temperature quantum heat current in different cases.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 10","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411073","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":"Correlation Entropy of Free Semigroup Actions","authors":"Xiaojiang Ye,&nbsp;Yanjie Tang,&nbsp;Dongkui Ma","doi":"10.1007/s10955-024-03348-y","DOIUrl":"10.1007/s10955-024-03348-y","url":null,"abstract":"<div><p>This paper introduces the concepts of correlation entropy and local correlation entropy for free semigroup actions on compact metric space, and investigates their underlying properties. Thereafter, we extend certain classical findings on correlation entropy and local correlation entropy to the realm of free semigroup actions. Finally, we establish the interconnections between topological entropy, measure-theoretic entropy, correlation entropy, and local correlation entropy for free semigroup actions under different conditions.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 10","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410628","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 a Planar Random Motion with Asymptotically Correlated Components","authors":"Manfred Marvin Marchione,&nbsp;Enzo Orsingher","doi":"10.1007/s10955-024-03337-1","DOIUrl":"10.1007/s10955-024-03337-1","url":null,"abstract":"<div><p>We study a planar random motion <span>(big (X(t),,Y(t)big ))</span> with orthogonal directions, where the direction switches are governed by a homogeneous Poisson process. At each Poisson event, the moving particle turns clockwise or counterclockwise according to a rule which depends on the current direction. We prove that the components of the vector <span>(big (X(t),,Y(t)big ))</span> can be represented as linear combinations of two independent telegraph processes with different intensities. The exact distribution of <span>(big (X(t),,Y(t)big ))</span> is then obtained both in the interior of the support and on its boundary, where a singular component is present. We show that, in the hydrodynamic limit, the process behaves as a planar Brownian motion with correlated components. The distribution of the time spent by the process moving vertically is then studied. We obtain its exact distribution and discuss its hydrodynamic limit. In particular, in the limiting case, the process <span>(big (X(t),,Y(t)big ))</span> spends half of the time moving vertically.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 10","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410497","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 Central Limit Theorem with Explicit Lyapunov Exponent and Variance for Products of (2times 2) Random Non-invertible Matrices","authors":"Audrey Benson,&nbsp;Hunter Gould,&nbsp;Phanuel Mariano,&nbsp;Grace Newcombe,&nbsp;Joshua Vaidman","doi":"10.1007/s10955-024-03335-3","DOIUrl":"10.1007/s10955-024-03335-3","url":null,"abstract":"<div><p>The theory of products of random matrices and Lyapunov exponents have been widely studied and applied in the fields of biology, dynamical systems, economics, engineering and statistical physics. We consider the product of an i.i.d. sequence of <span>(2times 2)</span> random non-invertible matrices with real entries. Given some mild moment assumptions we prove an explicit formula for the Lyapunov exponent and prove a central limit theorem with an explicit formula for the variance in terms of the entries of the matrices. We also give examples where exact values for the Lyapunov exponent and variance are computed. An important example where non-invertible matrices are essential is the random Hill’s equation, which has numerous physical applications, including the astrophysical orbit problem.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 10","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409357","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":"Localization in Boundary-Driven Lattice Models","authors":"Michele Giusfredi,&nbsp;Stefano Iubini,&nbsp;Paolo Politi","doi":"10.1007/s10955-024-03324-6","DOIUrl":"10.1007/s10955-024-03324-6","url":null,"abstract":"<div><p>Several systems display an equilibrium condensation transition, where a finite fraction of a conserved quantity is spatially localized. The presence of two conservation laws may induce the emergence of such transition in an out-of-equilibrium setup, where boundaries are attached to different and subcritical heat baths. We study this phenomenon in a class of stochastic lattice models, where the local energy is a general convex function of the local mass, mass and energy being both globally conserved in the isolated system. We obtain exact results for the nonequilibrium steady state (spatial profiles, mass and energy currents, Onsager coefficients) and we highlight important differences between equilibrium and out-of-equilibrium condensation.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 10","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-024-03324-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414232","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":"Equivariant Divergence Formula for Hyperbolic Chaotic Flows","authors":"Angxiu Ni,&nbsp;Yao Tong","doi":"10.1007/s10955-024-03329-1","DOIUrl":"10.1007/s10955-024-03329-1","url":null,"abstract":"<div><p>We prove the equivariant divergence formula for axiom A flow attractors. It is a pointwisely-defined and recursive formula for perturbation of SRB measures along center-unstable manifolds. It depends on only the zeroth and first order derivatives of the map, the observable, and the perturbation. Hence, the linear response acquires an ‘ergodic theorem’, which means that it can be sampled by recursively computing a few vectors on one orbit.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 9","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-024-03329-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248000","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":"Optimal Control of Underdamped Systems: An Analytic Approach","authors":"Julia Sanders,&nbsp;Marco Baldovin,&nbsp;Paolo Muratore-Ginanneschi","doi":"10.1007/s10955-024-03320-w","DOIUrl":"10.1007/s10955-024-03320-w","url":null,"abstract":"<div><p>Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an open and challenging research frontier, with a spectrum of applications ranging from stochastic thermodynamics to biophysics and data science. Among these, the design of nanoscale electronic components motivates the study of underdamped dynamics, leading to practical and conceptual difficulties. In this work, we develop analytic techniques to determine protocols steering finite time transitions at a minimum thermodynamic cost for stochastic underdamped dynamics. As cost functions, we consider two paradigmatic thermodynamic indicators. The first is the Kullback–Leibler divergence between the probability measure of the controlled process and that of a reference process. The corresponding optimization problem is the underdamped version of the Schrödinger diffusion problem that has been widely studied in the overdamped regime. The second is the mean entropy production during the transition, corresponding to the second law of modern stochastic thermodynamics. For transitions between Gaussian states, we show that optimal protocols satisfy a Lyapunov equation, a central tool in stability analysis of dynamical systems. For transitions between states described by general Maxwell-Boltzmann distributions, we introduce an infinite-dimensional version of the Poincaré-Lindstedt multiscale perturbation theory around the overdamped limit. This technique fundamentally improves the standard multiscale expansion. Indeed, it enables the explicit computation of momentum cumulants, whose variation in time is a distinctive trait of underdamped dynamics and is directly accessible to experimental observation. Our results allow us to numerically study cost asymmetries in expansion and compression processes and make predictions for inertial corrections to optimal protocols in the Landauer erasure problem at the nanoscale.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 9","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-024-03320-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248001","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":"Long-Time Anderson Localization for the Nonlinear Random Schrödinger Equation on ({mathbb {Z}}^d)","authors":"Hongzi Cong,&nbsp;Yunfeng Shi,&nbsp;Xiaoqing Wu","doi":"10.1007/s10955-024-03333-5","DOIUrl":"10.1007/s10955-024-03333-5","url":null,"abstract":"<div><p>In this paper, we prove the long-time Anderson localization for the nonlinear random Schrödinger equation on <span>({mathbb {Z}}^d)</span> by using the Birkhoff normal form technique.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 9","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248006","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 Behaviors of the Infinite Set of Lohe Hermitian Sphere Oscillators","authors":"Seung-Yeal Ha,&nbsp;Euntaek Lee","doi":"10.1007/s10955-024-03331-7","DOIUrl":"10.1007/s10955-024-03331-7","url":null,"abstract":"<div><p>We study the emergent behaviors of an infinite number of Lohe Hermitian sphere oscillators on the unit Hermitian sphere. For this, we propose an infinite analogue of the Lohe hermitian sphere model, and present sufficient frameworks leading to collective behaviors in terms of system parameters and initial data. Under some network topology, we show that practical synchronization emerges for a heterogeneous ensemble, whereas exponential synchronization can appear for a homogeneous ensemble. Furthermore we have also derived analogous results for the infinite swarm-sphere model. For the sender network topology in which coupling capacities depend only on the sender index number, we show that there are only two possible asymptotic states, namely complete phase synchrony or bi-cluster configuration for a homogeneous ensemble in a positive coupling regime.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"191 9","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142200391","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}