Journal of Statistical Physics最新文献_第2页

Analysis of Stochastic Chemical Reaction Networks with a Hierarchy of Timescales

IF 1.3 3区物理与天体物理

Journal of Statistical Physics Pub Date : 2025-03-10 DOI: 10.1007/s10955-025-03428-7

Lucie Laurence, Philippe Robert

引用次数: 0

RG Analysis of Spontaneous Stochasticity on a Fractal Lattice: Stability and Bifurcations

IF 1.3 3区物理与天体物理

Journal of Statistical Physics Pub Date : 2025-03-07 DOI: 10.1007/s10955-025-03425-w

Alexei A. Mailybaev

{"title":"RG Analysis of Spontaneous Stochasticity on a Fractal Lattice: Stability and Bifurcations","authors":"Alexei A. Mailybaev","doi":"10.1007/s10955-025-03425-w","DOIUrl":"10.1007/s10955-025-03425-w","url":null,"abstract":"<div>In this paper, we study the stability and bifurcations of spontaneous stochasticity using an approach reminiscent of the Feigenbaum renormalization group (RG). We consider dynamical models on a self-similar space-time lattice as toy models for multiscale motion in hydrodynamic turbulence. Here an ill-posed ideal system is regularized at small scales and the vanishing regularization (inviscid) limit is considered. By relating the inviscid limit to the dynamics of the RG operator acting on the flow maps, we explain the existence and universality (regularization independence) of the limiting solutions as a consequence of the fixed-point RG attractor. Considering the local linearized dynamics, we show that the convergence to the inviscid limit is governed by the universal RG eigenmode. We also demonstrate that the RG attractor undergoes a period-doubling bifurcation with parameter variation, thereby changing the nature of the inviscid limit. In the case of chaotic RG dynamics, we introduce the stochastic RG operator acting on Markov kernels. Then the RG attractor becomes stochastic, which explains the existence and universality of spontaneously stochastic solutions in the limit of vanishing noise. We study a linearized structure (RG eigenmode) of the stochastic RG attractor and its period-doubling bifurcation. Viewed as prototypes of Eulerian spontaneous stochasticity, our models explain its mechanism, universality and potential diversity.</div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143571097","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}

引用次数: 0

Efficient Approximation of the CREM Gibbs Measure and the Hardness Threshold

IF 1.3 3区物理与天体物理

Journal of Statistical Physics Pub Date : 2025-03-06 DOI: 10.1007/s10955-025-03411-2

Fu-Hsuan Ho

{"title":"Efficient Approximation of the CREM Gibbs Measure and the Hardness Threshold","authors":"Fu-Hsuan Ho","doi":"10.1007/s10955-025-03411-2","DOIUrl":"10.1007/s10955-025-03411-2","url":null,"abstract":"<div>The continuous random energy model (CREM) is a toy model of disordered systems introduced by Bovier and Kurkova in 2004 based on previous work by Derrida and Spohn in the 80s. In a recent paper by Addario-Berry and Maillard, they raised the following question: what is the threshold (beta _G), at which sampling approximately the Gibbs measure at any inverse temperature (beta >beta _G) becomes algorithmically hard? Here, sampling approximately means that the Kullback–Leibler divergence from the output law of the algorithm to the Gibbs measure is of order o(N) with probability approaching 1, as (Nrightarrow infty ), and algorithmically hard means that the running time, the numbers of vertices queries by the algorithms, is beyond of polynomial order. The present work shows that when the covariance function A of the CREM is concave, for all (beta >0), a recursive sampling algorithm on a renormalized tree approximates the Gibbs measure with running time of order (O(N^{1+varepsilon })). For A non-concave, the present work exhibits a threshold (beta _G<infty ) such that the following hardness transition occurs: (a) For every (beta le beta _G), the recursive sampling algorithm approximates the Gibbs measure with a running time of order (O(N^{1+varepsilon })). (b) For every (beta >beta _G), a hardness result is established for a large class of algorithms. Namely, for any algorithm from this class that samples the Gibbs measure approximately, there exists (z>0) such that the running time of this algorithm is at least (e^{zN}) with probability approaching 1. In other words, it is impossible to sample approximately in polynomial-time the Gibbs measure in this regime. Additionally, we provide a lower bound of the free energy of the CREM that could hold its value.</div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 3","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03411-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143554153","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}

引用次数: 0

A Probabilistic Representation of the Solution to a 1D Evolution Equation in a Medium with Negative Index

IF 1.3 3区物理与天体物理

Journal of Statistical Physics Pub Date : 2025-02-28 DOI: 10.1007/s10955-025-03418-9

Éric Bonnetier, Pierre Etoré, Miguel Martinez

引用次数: 0

Density-Induced Variations of Local Dimension Estimates for Absolutely Continuous Random Variables

IF 1.3 3区物理与天体物理

Journal of Statistical Physics Pub Date : 2025-02-15 DOI: 10.1007/s10955-025-03416-x

Paul Platzer, Bertrand Chapron

{"title":"Density-Induced Variations of Local Dimension Estimates for Absolutely Continuous Random Variables","authors":"Paul Platzer, Bertrand Chapron","doi":"10.1007/s10955-025-03416-x","DOIUrl":"10.1007/s10955-025-03416-x","url":null,"abstract":"<div>For any multi-fractal dynamical system, a precise estimate of the local dimension is essential to infer variations in its number of degrees of freedom. Following extreme value theory, a local dimension may be estimated from the distributions of pairwise distances within the dataset. For absolutely continuous random variables and in the absence of zeros and singularities, the theoretical value of this local dimension is constant and equals the phase-space dimension. However, due to uneven sampling across the dataset, practical estimations of the local dimension may diverge from this theoretical value, depending on both the phase-space dimension and the position at which the dimension is estimated. To explore such variations of the estimated local dimension of absolutely continuous random variables, approximate analytical expressions are derived and further assessed in numerical experiments. These variations are expressed as a function of 1. the random variables’ probability density function, 2. the threshold used to compute the local dimension, and 3. the phase-space dimension. Largest deviations are anticipated when the probability density function has a low absolute value, and a high absolute value of its Laplacian. Numerical simulations of random variables of dimension 1 to 30 allow to assess the validity of the approximate analytical expressions. These effects may become important for systems of moderately-high dimension and in case of limited-size datasets. We suggest to take into account this source of local variation of dimension estimates in future studies of empirical data. Implications for weather regimes are discussed.</div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 2","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10955-025-03416-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143423348","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}

引用次数: 0

Field Theoretic Renormalization Group in an Infinite-Dimensional Model of Random Surface Growth in Random Environment 随机环境中随机表面生长的无限维模型中的场论重正化群

IF 1.3 3区物理与天体物理

Journal of Statistical Physics Pub Date : 2025-02-14 DOI: 10.1007/s10955-025-03410-3

N. V. Antonov, A. A. Babakin, N. M. Gulitskiy, P. I. Kakin

{"title":"Field Theoretic Renormalization Group in an Infinite-Dimensional Model of Random Surface Growth in Random Environment","authors":"N. V. Antonov, A. A. Babakin, N. M. Gulitskiy, P. I. Kakin","doi":"10.1007/s10955-025-03410-3","DOIUrl":"10.1007/s10955-025-03410-3","url":null,"abstract":"<div>The influence of a random environment on the dynamics of a fluctuating rough surface is investigated using the field theoretic renormalization group. The environment motion is modelled by the stochastic Navier–Stokes equation, which includes both a fluid in thermal equilibrium and a turbulent fluid. The surface is described by the generalized Pavlik’s stochastic equation. As a result of the renormalizability requirement, the model necessarily involves an infinite number of coupling constants. The one-loop counterterm is derived in an explicit closed form. The corresponding renormalization group equations demonstrate the existence of three two-dimensional surfaces of fixed points in the infinite-dimensional parameter space. If the surfaces contain IR attractive regions, the model allows for a large-scale, long-time scaling behaviour. For the first surface (advection is irrelevant) the critical dimensions of the height field (Delta _{h}), the response field (Delta _{h'}) and the frequency (Delta _{omega }) are non-universal through the dependence on the effective couplings. For the other two surfaces (advection is relevant) these dimensions appear to be universal and are found exactly.</div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 2","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143423399","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}

引用次数: 0

Near-Critical and Finite-Size Scaling for High-Dimensional Lattice Trees and Animals 高维网格树和动物的近临界和有限大小扩展

IF 1.3 3区物理与天体物理

Journal of Statistical Physics Pub Date : 2025-02-14 DOI: 10.1007/s10955-025-03414-z

Yucheng Liu, Gordon Slade

引用次数: 0

A Tale of Three Approaches: Dynamical Phase Transitions for Weakly Bound Brownian Particles 三种方法的故事：弱约束布朗粒子的动态相变

IF 1.3 3区物理与天体物理

Journal of Statistical Physics Pub Date : 2025-02-07 DOI: 10.1007/s10955-025-03407-y

Lucianno Defaveri, Eli Barkai, David A. Kessler

{"title":"A Tale of Three Approaches: Dynamical Phase Transitions for Weakly Bound Brownian Particles","authors":"Lucianno Defaveri, Eli Barkai, David A. Kessler","doi":"10.1007/s10955-025-03407-y","DOIUrl":"10.1007/s10955-025-03407-y","url":null,"abstract":"<div>We investigate a system of Brownian particles weakly bound by attractive parity-symmetric potentials that grow at large distances as (V(x) sim |x|^alpha ), with (0< alpha < 1). The probability density function P(x, t) at long times reaches the Boltzmann–Gibbs equilibrium state, with all moments finite. However, the system’s relaxation is not exponential, as is usual for a confining system with a well-defined equilibrium, but instead follows a stretched exponential (e^{- textrm{const} , t^nu }) with exponent (nu =alpha /(2+alpha )), as we announced recently in a short letter. In turn, the stretched exponential relaxation is related to large-deviation theory, which is studied from three perspectives. First, we propose a straightforward and general scaling rate-function solution for P(x, t). This rate function displays anomalous time scaling and a dynamical phase transition. Second, through the eigenfunctions of the Fokker–Planck operator, we obtain, using the WKB method, more complete solutions that reproduce the rate function approach and provide important pre-exponential corrections. Finally, we show how the alternative path-integral formalism allows us to recover the same results, with the above rate function being the solution of the classical Hamilton–Jacobi equation describing the most probable path. Properties such as parity, the role of initial conditions, and the dynamical phase transition are thoroughly studied in all three approaches.</div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 2","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361910","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}

引用次数: 0

Heat Exchange for Oscillator Strongly Coupled to Thermal Bath

IF 1.3 3区物理与天体物理

Journal of Statistical Physics Pub Date : 2025-02-06 DOI: 10.1007/s10955-025-03408-x

Alex V. Plyukhin

{"title":"Heat Exchange for Oscillator Strongly Coupled to Thermal Bath","authors":"Alex V. Plyukhin","doi":"10.1007/s10955-025-03408-x","DOIUrl":"10.1007/s10955-025-03408-x","url":null,"abstract":"<div>The heat exchange fluctuation theorem (XFT) by Jarzynski and Wójcik (Phys Rev Lett 92:230602, 2004) addresses the setting where two systems with different temperatures are brought in thermal contact at time (t=0) and then disconnected at later time (tau ). The theorem asserts that the probability of an anomalous heat flux (from cold to hot), while nonzero, is exponentially smaller than the probability of the corresponding normal flux (from hot to cold). As a result, the average heat flux is always normal. In that way, the theorem demonstrates how irreversible heat transfer, observed on the macroscopic scale, emerges from the underlying reversible dynamics. The XFT was proved under the assumption that the coupling work required to connect and then disconnect the systems is small compared to the change of the internal energies of the systems. That condition is often valid for macroscopic systems, but may be violated for microscopic ones. We examine the validity of the XFT’s assumption for a specific model of the Caldeira–Leggett type, where one system is a single classical harmonic oscillator and the other is a thermal bath comprised of a large number of oscillators. The coupling between the system and the bath, which is bilinear, is instantaneously turned on at (t=0) and off at (t=tau ). For that model, we found that the assumption of the XFT can be satisfied only for a rather restricted range of parameters. In general, the work involved in the process is not negligible and the energy exchange may be anomalous in the sense that the internal energy of the system, which is initially hotter than the bath, may further increase.</div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 2","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143184845","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}

引用次数: 0

Birkhoff Normal Form and Long Time Existence for d-Dimensional Generalized Pochhammer–Chree Equation

IF 1.3 3区物理与天体物理

Journal of Statistical Physics Pub Date : 2025-02-06 DOI: 10.1007/s10955-025-03409-w

Hongzi Cong, Siming Li, Yingte Sun, Xiaoqing Wu

引用次数: 0