Journal of Statistical Physics最新文献

We suggest a method of discretization of the domain of dynamical systems based on observations. The method utilizes (varepsilon )-entropy, (varepsilon )-capacity, and the introduced (varepsilon )-information. It results in the partition of the system’s domain to the cells of equal diameters that allows representation of the system in the terms of discrete dynamics and its numerical analysis and modelling.

In this paper, we study a gas of (N gg 1 ) weakly interacting fermions. We describe the time evolution of states that are perturbations of the Fermi ball, and analyze the dynamics in particle-hole variables. Our main result states that, for small values of the coupling constant and for appropriate initial data, the effective dynamics of the momentum distribution is determined by a discrete collision operator of quantum Boltzmann form.

We study the moments of the absolute value of the characteristic polynomial of the real elliptic ensemble, including the case of the real Ginibre ensemble. We obtain asymptotics for all integral moments inside the real bulk to order (1+o(1)). In particular, for the real Ginibre ensemble, this extends known computations for even moments, and confirms a recent conjecture of Serebryakov and Simm [51] in the integral case. For the elliptic case, this generalizes computations of first two moments by Fyodorov [27] and Fyodorov and Tarnowski [33]. We additionally find uniform asymptotics for the multi-point correlations of the absolute value of the characteristic polynomial. Our proof relies on a relation between expectations for the absolute value of the characteristic polynomial and the real correlation functions, as well as an algebraic method of obtaining asymptotics for the behavior of these correlation functions near the diagonal.

In this paper, using important properties of uniformly convex functions, we prove several types of fundamental inequalities as Jensen, its modification Jensen-Mercer, conversion of Jensen inequality and the Hermite-Hadamard inequality for uniformly convex functions. As applications of the main results we obtain new bounds for the joint entropy as well as new estimates of the bounds involving p-logarithmic means and their particular cases.

The celebrated Takens’ embedding theorem provides a theoretical foundation for reconstructing the full state of a dynamical system from partial observations. However, the classical theorem assumes that the underlying system is deterministic and that observations are noise-free, limiting its applicability in real-world scenarios. Motivated by these limitations, we formulate a measure-theoretic generalization that adopts an Eulerian description of the dynamics and recasts the embedding as a pushforward map between spaces of probability measures. Our mathematical results leverage recent advances in optimal transport. Building on the proposed measure-theoretic time-delay embedding theory, we develop a computational procedure that aims to reconstruct the full state of a dynamical system from time-lagged partial observations, engineered with robustness to handle sparse and noisy data. We evaluate our measure-based approach across several numerical examples, ranging from the classic Lorenz-63 system to real-world applications such as NOAA sea surface temperature reconstruction and ERA5 wind field reconstruction.

We study S=1/2 quantum spin chains with shift-invariant and inversion-symmetric next-nearest-neighbor interaction, also known as zigzag spin chains. We completely classify the integrability and non-integrability of the above class of spin systems. We prove that in this class there are only two integrable models, a classical model and a model solvable by the Bethe ansatz, and all the remaining systems are non-integrable. Our classification theorem confirms that within this class of spin chains, there is no missing integrable model. This theorem also implies the absence of intermediate models with a finite number of local conserved quantities.

We study lattice spin systems and analyze the evolution of Gaussian concentration bounds (GCB) under the action of probabilistic cellular automata (PCA), which serve as discrete-time analogues of Markovian spin-flip dynamics. We establish the conservation of GCB and, in the high-noise regime, demonstrate that GCB holds for the unique stationary measure. Additionally, we prove the equivalence of GCB for the space-time measure and its spatial marginals in the case of contractive probabilistic cellular automata. Furthermore, we explore the relationship between (non)-uniqueness and GCB in the context of space-time Gibbs measures for PCA and illustrate these results with examples.

We adapt Stein’s method of diffusion approximations, developed by Barbour, to the study of chaotic dynamical systems. We establish an error bound in the functional central limit theorem with respect to an integral probability metric of smooth test functions under a functional correlation decay bound. For systems with a sufficiently fast polynomial rate of correlation decay, the error bound is of order (O(N^{-1/2})), under an additional condition on the linear growth of variance. Applications include a family of interval maps with neutral fixed points and unbounded derivatives, and two-dimensional dispersing Sinai billiards.

By decoupling forward and backward stochastic trajectories, we construct a family of martingales and work theorems for both overdamped and underdamped Langevin dynamics. Our results are made possible by an alternative derivation of work theorems that uses tools from stochastic calculus instead of path-integration. We further strengthen the equality in work theorems by evaluating expectations conditioned on an arbitrary initial state value. These generalizations extend the applicability of work theorems and offer new interpretations of entropy production in stochastic systems. Lastly, we discuss the violation of work theorems in far-from-equilibrium systems.

In this paper, we prove a fluctuation theorem for the occupation time of the multi-species stirring process on a lattice starting from a stationary distribution. Our result shows that the occupation times of different species interact with each other at the level of equilibrium fluctuation. The proof of our result utilizes the resolvent strategy introduced in [12]. A coupling relationship between the multi-species stirring process and an auxiliary process and a graphical representation of the auxiliary process play the key roles in the proof.