Journal of Statistical Physics最新文献

This work investigates the stochastic dynamics of Hamiltonian systems with hyperbolic structure under external noise. To overcome the conflict between the non-anticipative nature of stochastic solutions and the exponential dichotomies of the hyperbolic structure, we construct auxiliary processes that are distributionally equivalent to the original dynamics. This construction allows us to leverage both explicit stable/unstable splittings (when available) and the Oseledets decomposition provided by the Multiplicative Ergodic Theorem (in the fully stochastic case). Within this framework, we prove central limit theorems and functional central limit theorems for the time-integrated normal deviations, with limiting covariances given explicitly in terms of the system parameters. These results establish the distributional characterization of hyperbolic tori persistence under stochastic perturbations, illustrating how tools from stochastic analysis and ergodic theory yield precise answers to a classical problem in Hamiltonian dynamics.

Consider the convex hull of a collection of disjoint open discs with radii 1/2. The boundary of the convex hull consists of a finite number of line segments and arcs. Randomly choose a point in one of the arcs in the boundary so that the density of its distribution is proportional to the total arc measure. Attach a new disc at the chosen point so that it is outside of the convex hull and tangential to its boundary. Replace the original convex hull with the convex hull of all preexisting discs and the new disc. Continue in the same manner. Simulations show that disc clusters form long, straight, or slightly curved filaments with many small side branches and occasional macroscopic side branches. For a large number of discs, the shape of the convex hull is either an equilateral triangle or a quadrangle. Side branches play the role analogous to avalanches in sandpile models, one of the best-known examples of self-organized criticality (SOC). Our simulation and theoretical results indicate that the size of a branch obeys a power law, as expected of avalanches in sandpile models and similar “catastrophies” in other SOC models.

In this paper, we study the oriented swap process on the positive integers and its asymptotic properties. Our results extend a theorem by Angel, Holroyd, and Romik regarding the trajectories of particles in the finite oriented swap process. Furthermore, we study the evolution of the type of a particle at the leftmost position over time. Our approach relies on a relationship between multi-species particle systems and Hecke algebras, complemented by a detailed asymptotic analysis.

In this paper, we study the homogeneous multi-component Curie-Weiss-Potts model with (q ge 3) spins. The model is defined on the complete graph (K_{Nm}), whose vertex set is equally partitioned into m components of size N. For a configuration (sigma : {1, cdots , Nm} rightarrow {1, cdots , q},) the Gibbs measure is defined by

where (Z_{N, beta }) is the normalizing constant, and (beta >0) is the inverse-temperature parameter. The interaction coefficient is

where (J in (0, 1)) is the relative strength of inter-component interaction to intra-component interaction. We identify a dynamical phase transition at the critical inverse-temperature (beta _{s}(q)), which is the same threshold as for the one-component Potts model [5] and depends only on the number of spins q,  but is independent of the number of components m and relative interaction strength (J in (0, 1).) By extending the aggregate path method [19] to multi-component setting, we prove that the mixing time is (O(N log N)) in the subcritical regime (beta <beta _{s}(q).) In the supercritical regime (beta > beta _{s}(q),) we further show that the mixing time is exponential in N via a metastability analysis. This is the first result for the dynamical phase transition in the multi-component Potts model.

Quantum cross entropy is a measure of information that quantifies the difference between two quantum states. In this paper, we first define the local quantum cross entropy based on local quantum Bernoulli noises (LQBNs) and examine several of its relevant properties, including its relationships with local quantum entropy and local quantum relative entropy, as well as its non-negativity, asymmetry, monotonicity, and unitary invariance with respect to the second parameter. Then, we investigate the local quantum cross entropy between any local quantum state and the normalized identity operator. Finally, we research its application in local quantum data compression.

Two new interacting particle systems are introduced in this paper: dynamic versions of the asymmetric inclusion process (ASIP) and the asymmetric Brownian energy process (ABEP). Dualities and reversibility of these processes are proven, where the quantum algebra ({mathcal {U}}_q(mathfrak {su}(1,1))) and the Al-Salam–Chihara polynomials play a crucial role. Two hierarchies of duality functions are found, where the Askey-Wilson polynomials and Jacobi polynomials sit on top.

An analytically solvable cell fluid model with unrestricted cell occupancy, infinite-range Curie–Weiss–type attraction and short-range intra-cell repulsion is studied within the grand-canonical ensemble. Building on an exact single-integral representation of the grand partition function, we apply Laplace’s method to obtain asymptotically exact expressions for the pressure, density and equation of state. The phase diagram of the model exhibits a hierarchy of first-order phase transition lines, each terminating at a critical point. We determine the coordinates of the first five such points. Recasting the formalism in dimensionless variables highlights the explicit temperature dependence of all thermodynamic functions. This enables us to derive a closed-form expression for the entropy. The results reveal pronounced entropy minima around integer cell occupancies and reproduce density-anomaly isotherm crossings analogous to those in core-softened models.

We provide an analytical framework for analyzing the quality of stochastic Verlet-type integrators for simulating the Langevin equation. Focusing only on basic objective measures, we consider the ability of an integrator to correctly simulate two characteristic configurational quantities of transport, a) diffusion on a flat surface and b) drift on a tilted planar surface, as well as c) statistical sampling of a harmonic potential. For any stochastic Verlet-type integrator expressed in its configurational form, we develop closed form expressions to directly assess these three most basic quantities as a function of the applied time step. The applicability of the analysis is exemplified through twelve representative integrators developed over the past five decades, and algorithm performance is conveniently visualized through the three characteristic measures for each integrator. The GJ set of integrators stands out as the only option for correctly simulating diffusion, drift, and Boltzmann distribution in linear systems, and we therefore suggest that this general method is the one best suited for high quality thermodynamic simulations of nonlinear and complex systems, including for relatively high time steps compared to simulations with other integrators.

In this work, we investigate the phase behavior of single-site adsorption models on one-dimensional (1D) lattice at nonzero temperatures, incorporating long-range intermolecular interactions up to the 12th neighbor. A comparative analysis of the models with different intermolecular potentials such as monotonic repulsive and attractive potentials with varying rates of decay, as well as a non-monotonic Lennard–Jones and oscillating potentials is performed. To accurately determine the thermodynamic properties of these systems, a tensor network approach to the well-known transfer matrix method is implemented. Characteristics of the models calculated in such way satisfy the conditions of thermodynamic equilibrium and belong to a formally infinite, truly thermodynamic, system. Using this approach, we have confirmed the remnants of “devil’s staircase” of phase transitions at nonzero temperatures in 1D system with repulsive interactions monotonically decreasing as ({r}^{-p}), where (p=1, 2, 3). The cutoff radius of such interactions is shown to influence both the set of possible structures and their stability range. 1D systems with monotonically attractive, Lennard–Jones, and oscillating potentials demonstrate the first-order phase transition associated with condensation of lattice gas. In these cases, the type of intermolecular potential, the decay rate of the monotonic potential, and its cutoff radius do not qualitatively impact the phase behavior of the system. These results can be useful for an interpretation of experimental data in studies of adsorption in 1D adsorbents such as nanotubes and microporous solids.

Sinaĭ initiated the study of random walks with persistently positive area processes, motivated by shock waves in solutions to the inviscid Burgers’ equation. We find the precise asymptotic probability that the area process of a random walk bridge is an excursion. A key ingredient is an analogue of Sparre Andersen’s classical formula. The asymptotics are related to von Sterneck’s subset counting formulas from additive number theory. Our results sharpen bounds by Aurzada, Dereich and Lifshits and respond to a question of Caravenna and Deuschel, which arose in their study of the wetting model. In this context, Sinaĭ excursions are a class of random polymer chains exhibiting entropic repulsion.